• Signed Informed Consent Form

• Ability to comply with the study protocol, in the investigator's judgment

• Histologically or cytologically confirmed epithelial ovarian, fallopian tube or primary peritoneal cancer

• Platinum status, defined by disease progression during or following treatment with platinum-based chemotherapy within 6 months of completing therapy

• Measurable or non-measurable but evaluable disease per RECIST v1.1 {Previously irradiated lesions can be considered as measurable disease only if progressive disease has been unequivocally documented at that site since radiation.}

• Availability of a representative tumor specimen for exploratory biomarker research will be required for 12 patients (see Section 5.4.5 for information on tumor specimens)

• ECOG Performance Status of 0-1

• Life expectancy ≥ 3 months

• Adequate hematologic and end-organ function, defined by the following laboratory test results, obtained within 14 days prior to initiation of study treatment: ANC ≥ 1.5 ⋅ 109/L (1500/μL) without granulocyte colony-stimulating factor support; Lymphocyte count ≥ 0.5 ⋅ 109/L (500/μL); Platelet count ≥ 100 ⋅ 109/L (100,000/μL) without transfusion; Hemoglobin ≥ 80 g/L (8 g/dL) (Patients may be transfused to meet this criterion.)

‣ AST, ALT, and alkaline phosphatase (ALP) ≤ 2.5 ⋅ upper limit of normal (ULN), with the following exceptions:

• Patients with documented liver metastases: AST and ALT ≤ 5 ⋅ ULN

∙ Patients with documented liver or bone metastases: ALP ≤ 5 ⋅ ULN

⁃ Serum bilirubin ≤ 1.5 ⋅ ULN with the following exception:

• Patients with known Gilbert disease: serum bilirubin ≤ 3 ⋅ ULN

⁃ Serum creatinine ≤ 1.5 ⋅ ULN

⁃ Serum albumin ≥ 25 g/L (2.5 g/dL)

⁃ For patients not receiving therapeutic anticoagulation: INR or aPTT ≤ 1.5 ⋅ ULN

⁃ For patients receiving therapeutic anticoagulation: stable anticoagulant regimen

• Negative HIV test at screening, with the following exception: patients with a positive HIV test at screening are eligible if they are stable on anti-retroviral therapy, have a CD4 count \> 200, and have an undetectable viral load.

• Negative hepatitis B surface antigen (HBsAg) test at screening

• For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive methods as defined below:

‣ Women must remain abstinent or use contraceptive methods with a failure rate of \< 1% per year during the treatment period and for 5 months after the final dose of atezolizumab and for 24 months after the final dose of vismodegib. Women must refrain from donating eggs during this same period.

⁃ A woman is considered to be of childbearing potential if she is postmenarchal, has not reached a postmenopausal state (≥ 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). The definition of childbearing potential may be adapted for alignment with local guidelines or requirements.

⁃ Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices.

⁃ The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not adequate methods of contraception.