Advanced basal cell carcinomas (BCCs) circumvent Smoothened (SMO) inhibition by activating GLI transcription factors to sustain the high levels of Hedgehog (HH) signaling required for their survival. Unfortunately, there is a lack of efficacious therapies. We performed a gene expression–based drug repositioning screen in silico and identified the FDA-approved histone deacetylase (HDAC) inhibitor, vorinostat, as a top therapeutic candidate. We show that vorinostat only inhibits proliferation of BCC cells in vitro and BCC allografts in vivo at high dose, limiting its usefulness as a monotherapy. We leveraged this in silico approach to identify drug combinations that increase the therapeutic window of vorinostat and identified atypical PKC Ɩ/ʎ (aPKC) as a HDAC costimulator of HH signaling. We found that aPKC promotes GLI1-HDAC1 association in vitro, linking two positive feedback loops. Combination targeting of HDAC1 and aPKC robustly inhibited GLI1, lowering drug doses needed in vitro, in vivo, and ex vivo in patient-derived BCC explants. We identified a bioavailable and selective small-molecule aPKC inhibitor, bringing the pharmacological blockade of aPKC and HDAC1 into the realm of clinical possibility. Our findings provide a compelling rationale and candidate drugs for combined targeting of HDAC1 and aPKC in HH-dependent cancers.