Multicenter, double-blind, randomized, vehicle-controlled study that evaluates the efficacy and safety of patidegib gel 2% and 4% in comparison with vehicle in participants at least 18 years of age that meet the diagnostic criteria for basal cell nevus syndrome (BCNS). Participants will be randomized to receive patidegib gel 2%, patidegib gel 4%, or the vehicle gel for a 26-week treatment period.

Participants who meet the study entry criteria will be randomized in a 1:1:1 ratio to receive patidegib gel 2%, patidegib gel 4%, vehicle gel. One or two tubes of the assigned study drug will be dispensed to the participant at the Baseline visit. Additional tubes will be dispensed at subsequent visits through Week 22. The study drug will be applied topically to the entire face as well as to treatment-targeted surgically eligible basal cell carcinomas (SEBs) at other anatomical sites twice daily for 26 weeks of treatment.

Information on reported and observed adverse events will be obtained at each visit. An abbreviated physical examination will be performed at Baseline, Week 14, and Week 26.

At Baseline and Weeks 6, 10, 14, 18, 22, and 26, all visible basal cell carcinomas (BCCs) (excluding areas below the knees) will be identified by the Investigator, circled in ink, photographed, measured, and recorded on a body diagram. Treatment-targeted SEBs (defined as the 5 SEBs on the face and/or other anatomical areas identified at Baseline as SEBs) will be treated during the 26-week treatment phase. If a participant has 5 eligible previously untreated facial SEBs (excluding tumors on nose and eyelids) these tumors will be the participant's 5 baseline treatment-targeted SEBs and non-facial baseline SEBs will not be treated with study drug. Tumors to be measured and mapped include the 5 baseline treatment-targeted tumors as well as all other facial tumors including those on the eyelids and the nose. In addition, up to 10 non-treatment-targeted non-facial tumors will also be measured and mapped.

Inclusion Criteria:

1. The participant is from 18 to 85 years of age, inclusive.

2. The participant must provide written informed consent prior to any study procedures.

3. The participant must meet diagnostic criteria for BCNS, including the first listed major criterion below plus one additional major criterion, or the first listed major criterion below plus 2 of the minor criteria outlined below:

   Major Criteria:

   • More than 2 histologically confirmed BCCs or one under the age of 20 years
   • Odontogenic keratocysts of the jaw proven by histology
   • Three or more palmar and/or plantar pits
   • Bilamellar calcification of the falx cerebri (if less than 20 years old)
   • Fused, bifid, or markedly splayed ribs
   • First degree relative with basal cell nevus syndrome
   • Patched 1 (PTCH1) gene mutation in normal tissue

   Minor Criteria:

   • Macrocephaly
   • Congenital malformations: cleft lip or palate, frontal bossing, "coarse face", moderate or severe hypertelorism
   • Skeletal abnormalities: sprengel deformity, marked pectus deformity, or marked syndactyly of the digits
   • Radiological abnormalities: bridging of the sella turcica, vertebral anomalies such as hemivertebrae, fusion or elongation of the vertebral bodies, modeling defects of the hands and feet, or flame shaped lucencies of the hands or feet
   • Ovarian fibroma
   • Medulloblastoma

4. The participant must have a history of at least 10 BCCs in toto present at Baseline and/or treated within 24 months prior to screening.

5. The participant has at Baseline a total of at least 5 previously untreated SEBs (greatest diameter 5 millimeters [mm] or greater on the face excluding the nose and periorbital skin, 9 mm or greater on non-facial areas excluding the skin below the knees), as documented clinically by the Investigator at Baseline. Untreated is define as no previous surgical or topical or intralesional drug treatment. Previous treatment with systemically administered drugs more than 6 months prior to Baseline is not considered previous treatment as long as there was no clinical evidence of resistance to oral hedgehog (HH) pathway inhibitors (such as vismodegib, patidegib, and sonidegib). Baseline treatment-targeted SEBs must not exceed a diameter of >2 centimeters (cm). At least one of these tumors must be appropriate for a 2 mm punch biopsy for biomarker analysis at Baseline and Week 6 visits. If a participant has 5 or more facial, excluding periorbital and nasal skin, SEBs at Baseline, non-facial SEBs will not be treatment-targeted SEBs.

6. The participant is willing to have SEBs biopsied for biomarkers and plasma to be collected to measure drug levels as required in the protocol.

7. The participant is willing to abstain from application of non-study topical prescription and over the counter medications to facial skin and within 5 cm of treatment targeted SEBs at other anatomical areas for the duration of the study except as prescribed by the Investigator. Moisturizers and emollients are allowable. Participants will be encouraged to use sunscreen with a sunscreen protection factor (SPF) 15 or higher at least once daily on all exposed skin sites.

8. Female participants must have a negative serum pregnancy test at Screening.

9. If the participant is a male with a female sexual partner who is of childbearing potential the couple is willing to use two effective methods of birth control during the duration of the trial and for one month after the last application of the gel. A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (that is, has had menses at any time in the preceding 24 consecutive months), must agree to use 2 effective methods of contraception for the duration of the study and at least 1 month after the last study drug application. The two forms of birth control authorized are defined as the use of a barrier method of contraception (condom with spermicide) in association with one of the following methods of birth control: bilateral tubal ligation; combined oral contraceptives (estrogens and progesterone) or implanted or injectable contraceptives with a stable dose for at least 1 month prior to Baseline; hormonal intra-uterine device (IUD) inserted at least 1 month prior to Baseline.

10. The participant is willing to contact the study center after each primary skin care physician (PSCP) visit to provide the study center details of the visit and any treatment of skin tumors.

11. The participant is willing to forego treatment of the treatment targeted baseline SEBs except when the Investigator and/or primary care giver believes that delay in treatment potentially might compromise the health of the participant.

Exclusion Criteria:

1. The participant is a woman of childbearing potential. This proscription is based on the key role of the HH pathway in embryogenesis, the known preclinical teratogenic effects of systemic cyclopamine, a naturally occurring inhibitor of SMO, and the unknown level of systemic exposure following topical application in humans. A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (that is, has had menses at any time in the preceding 24 consecutive months).

2. The participant has used topical products to the face or within 5 cm of a treatment targeted SEB or systemic therapies that might interfere with the evaluation of the study medication during the study. Specifically, these include the use of:

   • Topical glucocorticoids 30 days prior to screening
   • Retinoids (such as etretinate, isotretinoin, tazarotene, tretinoin, adapalene) systemically or topically or > 5% of an alphahydroxy acid (such as glycolic acid, lactic acid) or 5-fluorouracil or imiquimod (except as topical treatment to discrete BCCs) systemically or topically to the skin during the 6 months prior to entry.
   • Systemic chemotherapy within one year prior to screening. (Note: field therapy with topically applied treatments can be done as long as they are not applied within 5 cm of a treatment targeted tumor).
   • Known inhibitors of the HH signaling pathway (such as vismodegib, patidegib, and sonidegib) topically or systemically within 6 months of entry into the study.

3. The participant has a history of hypersensitivity to any of the ingredients in the study drug formulation.

4. The participant is unable or unwilling to make a good faith effort to return for all follow-up visits and tests.

5. The participant has uncontrolled systemic disease.

6. The participant has clinically important history of liver disease, including viral hepatitis, current alcohol abuse, or cirrhosis.

7. The participant has any condition or situation which in the Investigator's opinion may put the participant at significant risk, could confound the study results, or could interfere significantly with the participant's participation in the study. This includes history of other skin conditions or diseases, metabolic dysfunction, physical examination findings, or clinical laboratory findings giving reasonable suspicion of a disease or condition that contraindicates use of an investigational drug or that might affect interpretation of the results of the study or render the participant at high risk from treatment complications.

8. The participant has a history of invasive cancer within the past 5 years excluding non-melanoma skin cancer, Stage I cervical cancer, ductal carcinoma in situ of breast, or chronic lymphocytic lymphoma (Stage 0).

9. The participant has current, recent (within 4 weeks of Baseline visit), or planned participation in an experimental drug study while enrolled in this study.

10. Female sexual partner(s) of male participants who are unwilling or unable to comply with pregnancy prevention measures.