Inclusion Criteria:

          -  Histologically confirmed triple negative breast cancer (TNBC) that is either locally
             recurrent, inoperable and cannot be treated with curative intent or is metastatic

          -  Documented disease progression occurring within 12 months from the last treatment with
             curative intent

          -  Prior treatment (of early breast cancer) with an anthracycline and taxane

          -  Have not received prior chemotherapy or targeted systemic therapy for their locally
             advanced inoperable or metastatic recurrence. Prior radiation therapy for recurrent
             disease is permitted

          -  Measurable or non-measurable disease, as defined by RECIST 1.1

          -  Availability of a representative formalin-fixed paraffin-embedded (FFPE) tumour block
             (preferred) or at least 17 unstained slides, collected within 3 months prior to
             randomisation, with an associated pathology report, if available. If a tumour sample
             taken within 3 months before randomisation is not available and a tumour biopsy is not
             clinically feasible, the primary surgical resection sample or the most recent FFPE
             tumour biopsy sample may be used. Of these additional options, the most recent sample
             should be used.

          -  Eastern Cooperative Oncology Group performance status 0-1

          -  Life expectancy ≥ 12 weeks

          -  Adequate haematologic and end-organ function

          -  Negative human immunodeficiency virus (HIV) test ---Negative hepatitis B surface
             antigen (HBsAg) test at screening

          -  Negative total hepatitis B core antibody (HBcAb) test at screening, or positive HBcAb
             test followed by a negative hepatitis B virus (HBV) DNA test at screening

          -  The HBV DNA test will be performed only for patients who have a negative HBsAg and a
             positive HBcAb test.

          -  Negative hepatitis C virus (HCV) antibody test at screening, or positive HCV antibody
             test followed by a negative HCV RNA test at screening.

          -  Women of childbearing potential must agree to remain abstinent (refrain from
             heterosexual intercourse) or use a contraceptive method with a failure rate of ≤1% per
             year during the treatment period and for at least 5 months after the last dose of
             atezolizumab or 6 months after the last dose of capecitabine, whichever is later. In
             addition, women must refrain from donating eggs during the same time period.

          -  Men must agree to remain abstinent (refrain from heterosexual intercourse) or use
             contraceptive measures, and agree to refrain from donating sperm

        Inclusion criteria for patients enrolled after the recruitment of all-comers is complete:

        -PD-L1-positive tumour status (assessed centrally prior to randomisation), defined as PD-L1
        expression on tumour-infiltrating immune cells (IC) of 1% or greater.

        Exclusion Criteria:

          -  Spinal cord compression not definitively treated with surgery and/or radiation, or
             previously diagnosed and treated spinal cord compression without evidence that disease
             has been clinically stable for > 2 weeks prior to randomisation

          -  Symptomatic, untreated, or actively progressing central nervous system (CNS)
             metastases.

          -  Symptomatic or rapid visceral progression

          -  No prior treatment with an anthracycline and taxane

          -  History of leptomeningeal disease

          -  Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent
             drainage procedures (once monthly or more frequently) (patients with indwelling
             catheters such as PleurX® are allowed)

          -  Uncontrolled tumour-related pain

          -  Uncontrolled or symptomatic hypercalcemia

          -  Malignancies other than TNBC within 5 years prior to randomisation)

          -  Significant cardiovascular disease, within 3 months prior to randomisation, unstable
             arrhythmias, or unstable angina

          -  Presence of an abnormal ECG

          -  Severe infection requiring oral or IV antibiotics within 4 weeks prior to
             randomisation, including but not limited to hospitalization for complications of
             infection, bacteraemia, or severe pneumonia.

          -  Current treatment with anti-viral therapy for HBV.

          -  Major surgical procedure within 4 weeks prior to randomisation or anticipation of the
             need for a major surgical procedure during the course of the study other than for
             diagnosis

          -  Treatment with investigational therapy within 28 days prior to randomisation

          -  Pregnant or lactating, or intending to become pregnant during or within 5 months after
             the last dose of atezolizumab, or within 6 months after the last dose of capecitabine,
             whichever is later.

        Exclusion Criteria Related to Atezolizumab:

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

          -  Known hypersensitivity or allergy to biopharmaceuticals produced in Chinese hamster
             ovary cells or to any component of the atezolizumab formulation

          -  History of autoimmune disease

          -  Prior allogeneic stem cell or solid organ transplantation

          -  History of idiopathic pulmonary fibrosis (including pneumonitis), drug-induced
             pneumonitis, organizing pneumonia (i.e. bronchiolitis obliterans, cryptogenic
             organizing pneumonia), or evidence of active pneumonitis on screening chest
             computerised tomography (CT) scan History of radiation pneumonitis in the radiation
             field (fibrosis) is permitted.

          -  Active tuberculosis

          -  Receipt of a live, attenuated vaccine within 4 weeks prior to randomisation or
             anticipation that a live, attenuated vaccine will be required during
             atezolizumab/placebo treatment or within 5 months after the last dose of
             atezolizumab/placebo

          -  Prior treatment with CD137 agonists, anti-PD-1, or anti-PD-L1 therapeutic antibody or
             pathway targeting agents

          -  Treatment with systemic immunostimulatory agents (including but not limited to
             interferons or interleukin [IL]-2) within 4 weeks or five half-lives of the drug
             (whichever is longer) prior to randomisation

          -  Treatment with systemic corticosteroids or other systemic immunosuppressive
             medications within 2 weeks prior to randomisation, or anticipated requirement for
             systemic immunosuppressive medications during the trial

        Exclusion Criteria Related to Capecitabine:

          -  Inability to swallow pills

          -  Malabsorption syndrome, disease significantly affecting gastrointestinal function,
             resection of the stomach or small bowel, or ulcerative colitis

          -  Known dihydropyrimidine dehydrogenase (DPD) deficiency or history of severe and
             unexpected reactions to fluoropyrimidine therapy in patients selected to receive
             capecitabine

        Exclusion Criteria Related to Carboplatin/Gemcitabine:

        -Hypersensitivity to platinum containing compounds or any component of carboplatin or
        gemcitabine drug formulations in patients selected to receive carboplatin and Gemcitabine