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