Topical Remetinostat in Treating Patient With Cutaneous Basal Cell Cancer

Inclusion Criteria: * Must have at least one BCC lesion \> 1 cm (BCC \> 5 mm) in non-cosmetically sensitive site(s) * Must be willing to apply the topical remetinostat 3 times daily for 6 weeks * For women of child bearing potential, a negative urine pregnancy test * Women of child bearing potential are expected to use an effective method of birth control while participating in the study and for 1 month after applying the last dose * For male subjects with female partners of childbearing potential, agreement to use adequate contraception while participating in the study and for 1 month after applying the last dose * Has signed and dated the current Institutional Review Board (IRB) approved informed consent document Exclusion Criteria: * Taking any medication known to interact with histone deacetylase (HDAC) inhibitors, such as valproate or anticoagulants * Taking any medication known to affect hedgehog (HH) signaling pathway such as itraconazole * Within the past 6 months, has used topical or systemic therapies that might interfere with the evaluation of the study medication during the study; specifically, these include the topical use to the study tumors of: * Glucocorticoids * Retinoids either systemically or topically (eg, etretinate, isotretinoin, tazarotene, tretinoin, adapalene) * Alpha hydroxy acids (eg, glycolic acid, lactic acid) to \> 5% of the skin * 5 fluorouracil or imiquimod and/or * Itraconazole * Has received treatment with systemic chemotherapy or agents known to be inhibitors of HH signaling, within 60 days to starting study medication * Currently receiving systemic medications that could affect BCC tumors (eg, oral retinoids) or might interact with remetinostat * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, recurrent seizure history or psychiatric illness/social situations that would limit compliance with study requirements * Moderate to severe immunosuppression due to disease or medication * Known or previous hypersensitivity to histone deacetylase inhibitor (HDACi) * History of congestive heart failure; cardiac arrhythmias; or other findings of ventricular dysfunction * History of current evidence of malabsorption or liver disease * Pregnancy or breast feeding