Inclusion Criteria:

          -  Histologically confirmed urothelial carcinoma of the bladder, ureter, urethra, or
             renal pelvis by the enrolling institution. Patients with mixed histologies are
             required to have a predominant urothelial component as reviewed by the pathologist at
             the enrolling institution.

          -  Locally advanced (T4b, any N: any T, N2-3) or metastatic (M1) disease as determined by
             the treating investigator.

          -  Age ≥18 years

          -  Life expectancy ≥ 12 weeks

          -  The patient must have measurable disease according to RECIST v1.1 and must have one
             site amenable to biopsy that, in the opinion of the investigator and/or interventional
             radiologist, is likely to yield acceptable tumor sample for a core biopsy per the
             below pathology criteria.

          -  Subject must agree to undergo two research-directed biopsies during treatment.

          -  Patients must have adequate tumor tissue available for PD-L1 testing. Adequate tumor
             tissue is defined as:

               -  For core-needle biopsy specimens, at least three cores should be submitted for
                  evaluation if feasible. Acceptable samples include core-needle biopsies for deep
                  tumor tissue (minimum of three cores) or excisional, incisional, punch, or
                  forceps biopsies for cutaneous, subcutaneous, or mucosal lesions. Samples
                  collected from fine-needle aspiration, brushing, cell pellet from pleural
                  effusion, bone metastases without a soft tissue component, and lavage are not
                  acceptable.

               -  For pre-treatment archival tissue, representative urothelial carcinoma FFPE tumor
                  specimens (tumor blocks or 30 unstained slides) must be provided. Patients with <
                  30 slides may be enrolled after discussion with the MSK Principal Investigator.

               -  Primary or metastatic specimens (with the exception of bone because it is not
                  evaluable for PD-L1 expression) may be submitted.

          -  Adequate hematologic and end organ function, defined by the following laboratory
             results obtained within 14 days prior to the first study treatment (Cycle 1, Day 1):

               -  ANC ≥ 1500 cells/uL

               -  WBC counts > 2500/uL

               -  Lymphocyte count ≥ 300/uL

               -  Platelet count ≥ 100,000/uL; Hemoglobin ≥ 9.0 g/dL

               -  Total bilirubin ≤ 1.5 x upper limit of normal (ULN) with the following exception:

               -  Patients with known Gilbert disease who have total bilirubin level ≤ 3 x ULN may
                  be enrolled.

          -  AST and ALT ≤ 3.0 x ULN with the following exception:

             °Patients with liver metastases may enroll with AST and ALT ≤ 5 x ULN

          -  Alkaline phosphatase ≤ 2.5 x ULN with the following exception:

             °Patients with documented liver or bone metastases may enroll with alkaline
             phosphatase ≤ 5 x ULN

          -  Estimated glomerular filtration rate (eGFR) ≥ 50 ml/min/1.73m^2 using the CKD-EPI
             equation: eGFR = 141 x min(Scr/k, 1)a x max(Scr/k, 1)-1.209 x 0.993Age x 1.018 [if
             female] x 1.159 [if black] Scr is serum creatinine, k is 0.7 for females and 0.9 for
             males, a is -0.329 for females and -0.411 for males, min indicates the minimum of
             --Scr/k or 1, and max indicates the maximum of Scr/k or 1

          -  For female patients of childbearing potential and male patients with partners of
             childbearing potential, agreement (by patient and/or partner) to use highly effective
             form(s) of contraception (i.e., one that results in a low failure rate [< 1% per year]
             when used consistently and correctly) and to continue its use for 5 months after the
             last dose of atezolizumab.

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1

          -  INR and aPTT ≤ 1.5 x ULN

               -  This applies only to patients who do not receive therapeutic anticoagulation;
                  patients receiving therapeutic anticoagulation (such as low-molecular-weight
                  heparin or warfarin) should be on a stable dose.

          -  Ability and willingness to comply with the requirements of the study protocol

        Exclusion Criteria:

          -  Prior chemotherapy or immunotherapy for metastatic urothelial cancer. Prior
             neoadjuvant or adjuvant chemotherapy with first progression > 12 months is allowed.
             Prior intravesical treatments such as BCG are allowed, however no BCG is allowed
             within 4 weeks prior to initiation of study treatment.

          -  Any approved anticancer therapy, including chemotherapy, hormonal therapy, or
             radiotherapy, within 3 weeks prior to initiation of study treatment; however, the
             following are allowed:

               -  Hormone-replacement therapy or oral contraceptives

               -  Herbal therapy > 1 week prior to Cycle 1, Day 1. Herbal therapy intended as
                  anticancer therapy must also be discontinued at least 1 week prior to Cycle 1,
                  Day 1.

               -  Palliative radiotherapy for bone metastases > 2 weeks prior to Cycle 1, Day 1

          -  Bisphosphonate therapy for symptomatic hypercalcemia

             °Use of bisphosphonate therapy for other reasons (e.g., bone metastasis or
             osteoporosis) is allowed.

          -  Known clinically significant liver disease, including active viral, alcoholic, or
             other hepatitis; cirrhosis; fatty liver; and inherited liver disease

          -  Patients with a history of or active bone marrow disorders expected to interfere with
             study therapy (e.g. acute leukemias, accelerated/blast-phase chronic myelogenous
             leukemia, chronic lymphocytic leukemia, Burkitt lymphoma, plasma cell leukemia, or
             non-secretory myeloma)

          -  Known primary central nervous system (CNS) malignancy or symptomatic CNS metastases

               -  Evaluable or measurable disease outside the CNS

               -  No metastases to brain stem, midbrain, pons, medulla, cerebellum, or within 10 mm
                  of the optic apparatus (optic nerves and chiasm)

               -  No history of intracranial hemorrhage or spinal cord hemorrhage

               -  No ongoing requirement for dexamethasone for CNS disease; patients on a stable
                  dose of anticonvulsants are permitted.

               -  No neurosurgical resection or brain biopsy within 28 days prior to Cycle 1, Day 1

          -  Patients with asymptomatic treated CNS metastases may be enrolled, provided all the
             criteria listed above are met as well as the following:

        Radiographic demonstration of improvement upon the completion of CNS-directed therapy and
        no evidence of interim progression between the completion of CNS-directed therapy and the
        screening radiographic study No stereotactic radiation or whole-brain radiation within 28
        days prior to Cycle 1, Day 1 Screening CNS radiographic study ≥ 4 weeks from completion of
        radiotherapy and ≥ 2 weeks from discontinuation of corticosteroids

          -  Pregnancy, lactation, or breastfeeding.

          -  Evidence of NYHA functional class III or IV heart disease

          -  Sensory or motor peripheral neuropathy ≥ grade 2

          -  Hearing loss ≥ grade 2

          -  Known hypersensitivity to Chinese hamster ovary cell products or other recombinant
             human antibodies

          -  History or risk of autoimmune disease, including but not limited to systemic lupus
             erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis
             associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's
             syndrome, Bell's palsy, Guillain-Barré syndrome, multiple sclerosis, autoimmune
             thyroid disease, vasculitis, or glomerulonephritis. The following are exceptions to
             this criterion.

               -  Patients with a history of autoimmune hypothyroidism on a stable dose of thyroid
                  replacement hormone may be eligible.

               -  Patients with controlled Type 1 diabetes mellitus on a stable insulin regimen may
                  be eligible.

          -  Patients with celiac disease controlled on diet alone may be eligible

          -  Patients with eczema, psoriasis, lichen simplex chronicus of vitiligo with
             dermatologic manifestations only (e.g., patients with psoriatic arthritis would be
             excluded) are permitted provided that they meet the following conditions:

               -  Patients with psoriasis must have a baseline ophthalmologic exam to rule out
                  ocular manifestations

               -  Rash must cover less than 10% of body surface area (BSA)

               -  Disease is well controlled at baseline and only requiring low potency topical
                  steroids (e.g., hydrocortisone 2.5%, hydrocortisone butyrate 0.1%, flucinolone
                  0.01%, desonide 0.05%, aclometasone dipropionate 0.05%)

               -  No acute exacerbations of underlying condition within the last 12 months (i.e.
                  not requiring psoralen plus ultraviolet A radiation [PUVA], methotrexate,
                  retinoids, biologic agents, oral calcineurin inhibitors; high potency or oral
                  steroids)

          -  History of idiopathic pulmonary fibrosis, pneumonitis (including drug induced),
             organizing pneumonia (i.e., bronchiolitis obliterans, cryptogenic organizing
             pneumonia, etc.), or evidence of active pneumonitis on screening chest computed
             tomography (CT) scan

             °History of radiation pneumonitis in the radiation field (fibrosis) is permitted.

          -  Any other diseases, metabolic dysfunction, physical examination finding, or clinical
             laboratory finding giving reasonable suspicion of a disease or condition that
             contraindicates the use of an investigational drug or that may affect the
             interpretation of the results or render the patient at high risk from treatment
             complications

          -  History of HIV infection or active hepatitis B (chronic or acute) or hepatitis C
             infection

               -  Patients with past or resolved hepatitis B infection (defined as having a
                  negative hepatitis B surface antigen [HBsAg] test and a positive anti-HBc
                  [antibody to hepatitis B core antigen] antibody test) are eligible.

               -  Patients positive for hepatitis C virus (HCV) antibody are eligible only if
                  polymerase chain reaction (PCR) is negative for HCV RNA.

          -  Active tuberculosis

          -  Severe infections within 4 weeks prior to Cycle 1, Day 1, including but not limited to
             hospitalization for complications of infection, bacteremia, or severe pneumonia

          -  Signs or symptoms of infection within 2 weeks prior to Cycle 1, Day 1

          -  Received oral or IV antibiotics within 2 weeks prior to Cycle 1, Day 1 °Patients
             receiving prophylactic antibiotics (e.g., for prevention of a urinary tract infection
             or chronic obstructive pulmonary disease) are eligible.

          -  Major surgical procedure within 28 days prior to Cycle 1, Day 1 or anticipation of
             need for a major surgical procedure during the course of the study

          -  Administration of a live, attenuated vaccine within 4 weeks before Cycle 1, Day 1 or
             anticipation that such a live, attenuated vaccine will be required during the study

             °Influenza vaccination should be given during influenza season only (approximately
             October to March). Patients must not receive live, attenuated influenza vaccine (e.g.,
             FluMist®) within 4 weeks prior to Cycle 1, Day 1 or at any time during the study.

          -  Malignancies other than the disease under study within 5 years prior to Cycle 1, Day
             1, with the exception of those with a negligible risk of metastasis or death and with
             expected curative outcome (such as but not limited to adequately treated carcinoma in
             situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer
             treated surgically with curative intent, or ductal carcinoma in situ treated
             surgically with curative intent) or undergoing active surveillance per
             standard-of-care management (e.g., chronic lymphocytic leukemia Rai Stage 0, prostate
             cancer with Gleason score ≤ 6, and prostate-specific antigen [PSA] ≤ 10 mg/mL, etc.)

          -  Prior treatment with anti-PD-1, or anti-PD-L1 therapeutic antibody or
             pathway-targeting agents

             °Patients who have received prior treatment with anti-CTLA-4 may be enrolled, provided
             the following requirements are met: Minimum of 12 weeks from the first dose of
             anti-CTLA-4 and > 6 weeks from the last dose No history of severe immune-related
             adverse effects from anti-CTLA-4 (NCI CTCAE Grade 3 and 4)

          -  Treatment with systemic immunostimulatory agents (including but not limited to
             interferon [IFN]-a or interleukin [IL]-2) within 6 weeks or five half-lives of the
             drug (whichever is shorter) prior to Cycle 1, Day 1

          -  Treatment with investigational agent within 4 weeks prior to Cycle 1, Day 1 (or within
             five half-lives of the investigational product, whichever is longer)

          -  Treatment with systemic immunosuppressive medications (including but not limited to
             prednisone, cyclophosphamide, azathioprine, methotrexate, thalidomide, and anti-tumor
             necrosis factor [anti-TNF] agents) within 2 weeks prior to Cycle 1, Day 1

               -  Patients who have received acute, low-dose, systemic immunosuppressant
                  medications (e.g., a one-time dose of dexamethasone for nausea) may be enrolled.

               -  The use of inhaled corticosteroids and mineralocorticoids (e.g., fludrocortisone)
                  is allowed.

          -  History of severe allergic, anaphylactic, or other hypersensitivity reactions to
             chimeric or humanized antibodies or fusion proteins

          -  Patients with prior allogeneic bone marrow transplantation or prior solid organ
             transplantation