This is a Phase II, 18 month, double blind, randomized placebo-controlled, two arm multicenter clinical study design. During the 18-month treatment period, the safety and chemopreventive efficacy of 150 mg/day GDC-0449 versus placebo will be assessed, and include evaluations of the skin at monthly intervals for the first three months and then every 3 months for the next 15 months. Removal of new surgically eligible BCCs (SEBs) will be done by primary skin care physicians (PSCPs) or at Study Centers. A Data Safety Monitoring Board (DSMB) will review unblinded results for an interim analysis when 20 subjects have completed 12 months of drug. This review will focus on adverse events and efficacy results. Subjects will be monitored for the development of new SEBs after they discontinue study treatment. At the end of the 18 months, given that the observed adverse events are minimal, patients on placebo will be offered the opportunity to take GDC-0449 for 18 months in an open label continuation, followed by six months observation, and patients on GDC449 will be monitored for the next 24 months for assessment of the duration of benefit after stopping the drug.