Inclusion Criteria:

          -  Subjects or their legally authorized representative must be informed of the
             investigational nature of this study, and must sign and give written informed consent
             in accordance with institutional and federal guidelines.

          -  Patients must have histologically proven urothelial carcinoma of the bladder. Those
             with mixed histology, including a component of urothelial carcinoma, are eligible.
             Pure small cell carcinoma, pure adenocarcinoma, and pure squamous cell carcinoma are
             excluded.

          -  Patients must have Stage cT2-T4a N0 M0 disease. Clinical T stage is based on the TURBT
             sample, exam under anesthesia and cross-sectional imaging studies. Patients must
             undergo cystoscopy and TURBT as part of the staging procedure within 120 days prior to
             registration.

        To exclude non-bulky/low-risk tumors, subjects must have documented muscle invasion with at
        least one of the following:

        i. Disease measuring at least 10 mm on cross-sectional imaging. Bladder thickening on
        imaging, by itself, is not adequate.

        ii. The presence of tumor-associated hydronephrosis.

          -  Patients must have staging scans with abdominal/pelvic CT or MRI scan, and CT scan or
             x-ray of the chest within 56 days prior to registration. If the alkaline phosphatase
             is > 1.5 x upper limit of normal (ULN), there is a presence of suspicious bone pain,
             or if there is other clinical suspicion of bone metastases, a whole body bone scan is
             required within 56 days prior to registration.

          -  Patients must have a Zubrod performance status of 0, 1 or 2.

          -  Patients must be 18 years of age or older.

          -  Patients must have adequate renal function as evidenced by calculated creatinine
             clearance ≥ 50 mL/min. The serum creatinine value used in the calculation must have
             been obtained within 28 days prior to registration.

          -  Patients must have adequate hepatic function (within 28 days prior to registration),
             defined as:

             i. Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (or ≤ 2.5 x ULN
             with Gilbert's disease); and ii. SGOT (AST) ≤ 2 x institutional ULN; and iii. SGPT
             (ALT) ≤ 2 x institutional ULN.

          -  Patients must have adequate hematologic function (within 28 days prior to
             registration), defined as:

             i. Absolute neutrophil count (ANC) ≥ 1,500/μL; and ii. Hemoglobin ≥ 9 g/dL; and iii.
             Platelets ≥ 100,000/μL.

          -  Patients must have tumor tissues from transurethral resection of the bladder tumor
             (TURBT) that is within 120 days of registration and available for submission. Tissue
             sample must be sufficient for IHC testing; that is,it must be sufficient tumor tissues
             for correlative science after pathologic diagnosis [i.e., enough tumor tissue to pass
             the staging criteria in 4c].

          -  Patients must consent to the submission of FFPE blocks and/or unstained slides.

        Exclusion Criteria:

          -  Patients must not have received previous systemic cytotoxic chemotherapy for
             urothelial carcinoma.

          -  Patients must not have peripheral neuropathy ≥ Grade 2.

          -  Patients must not have presence of Class III or IV heart failure, according to New
             York Heart Association Classifications, or a known left ventricular ejection fraction
             of less than 50%. Note: LVEF evaluation by echocardiogram or multi-gated acquisition
             scan (MUGA) is not required prior to registration.

          -  Patients must not have a significant history of bleeding events. Patients with a
             history of a significant bleeding episode (e.g. hemoptysis, upper or lower GI
             bleeding, grade 3 or 4 gross hematuria unable to be controlled by trans-urethral
             resection of the bladder tumor) within 6 months of registration are not eligible.

          -  No arterial thrombotic events within 6 months of registration, including transient
             ischemic attack (TIA), cerebrovascular accident (CVA), peripheral arterial thrombus,
             unstable angina or angina requiring surgical or medical intervention in the past 6
             months, or myocardial infarction (MI). Patients with clinically significant peripheral
             artery disease (i.e., claudication on less than one block) are ineligible.

        Patients who have experienced a deep venous thrombosis or pulmonary embolus within the past
        6 months must be on stable therapeutic anticoagulation to be enrolled to this study.

          -  In the opinion of the treating investigator, the patient must be a candidate to
             receive gemcitabine/cisplatin treatment.

          -  Patients must not have aspirin sensitive asthma.

          -  Patients must not be known to have hypersensitivity to cisplatin, gemcitabine, or
             celecoxib.

          -  Patients must not have any incidence of or uncontrolled medical illness (e.g. active
             cardiac symptoms, active systemic infection, etc.) that would limit the patient's
             ability to participate in the protocol.

          -  Patients must not be pregnant or nursing due to the potential teratogenic side effects
             of the protocol treatment. Women/men of reproductive potential must agree to use an
             effective contraceptive method during and for 6 months after completing protocol
             treatment. A negative pregnancy test is required within 7 days prior to registration
             for women of child-bearing potential.

          -  Patients are ineligible if they plan on regular use of NSAIDs at any dose more than 2
             times per week (on average) or aspirin at more than 325 mg at least three times per
             week, on average. Low-dose aspirin not exceeding 100 mg/day is permitted. Patients who
             agree to stop regular NSAIDs or higher dose aspirin are eligible and no wash out
             period is required.