The purpose of this study is to compare how well tolerated and effective four different dosing schedules (two personalized, intermittent dosing schedules as compared to a fixed intermittent and continuous dosing regimen) work in people with advanced basal cell carcinoma.

Inclusion Criteria:

• Patients with a cytologically or histologically confirmed locally advanced basal cell carcinoma. (Nodal involvement permitted)
• Adult males or females 18 years of age or older at time of signing informed consent. All races and ethnicities are eligible, and no upper limit of age is specified.
• Must have ability to comprehend and the willingness to sign written informed consent for study participation.
• Patients must have at least one cutaneous tumor site amenable to direct and accurate measurement by ruler/calipers.
• Patients may have received prior hedgehog inhibitor therapy (if more than 6 months prior) or other systemic treatments for basal cell carcinoma in the past.
• Eastern Cooperative Oncology Group (ECOG) performance status ≤2
• Agreement not to donate blood or blood products during the study and for 24 months after discontinuation of vismodegib.
• Patients must have adequate hepatic, renal, and bone marrow function as defined in the protocol.
• Participants must have a negative serum pregnancy test within 7 days prior to commencement of dosing in premenopausal women. Women of non-childbearing potential may be included without serum pregnancy test if they are either surgically sterile or have been postmenopausal for ≥1 year.
• Women of reproductive potential are required to use two forms of acceptable contraception (including one acceptable barrier method with spermicide) during therapy and for 24 months after completing therapy.
• Female patients must agree not to become pregnant or donate lactation during treatment and until 24 months after stop of treatment. Male patients must use condoms at all times, even after a vasectomy, during sexual intercourse with female partners of reproductive potential during treatment with vismodegib and for 3 months after the last dose to avoid exposing a pregnant partner and unborn fetus to vismodegib. Male patients must agree not to donate sperm during the study and for 3 months after discontinuation of vismodegib.

Exclusion Criteria:

• Received prior hedgehog inhibitor therapy in the last 6 months
• Female patients who are pregnant, intend to become pregnant or are nursing.
• Uncontrolled intercurrent illness including, but not limited to, serious infection. Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification.
• Previous malignancy is not an exclusion provided that the other malignancy is considered under control, patient is not on concomitant anti-cancer drug therapy, and target lesions from melanoma are clearly defined for response assessment.
• Inability or unwillingness to swallow capsules.
• Any known allergy, hypersensitivity or severe reaction to vismodegib or any of the ingredients
• Co-treatment with a statin or St. John's Wort.