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