ABSTRACT There are few confirmed black holes with a mass of less and no neutron stars with masses greater than , creating a gap in the observed distribution of compact star masses. We present new optical photometry of the Low mass X-ray binary V1408 Aql, which is a persistent X-ray source thought to contain a black hole. The optical light curve of V1408 Aql shows nearly sinusoidal modulations at the orbital period, superimposed on large night-to-night variations. We combined this photometry with previously published photometry to derive a more precise orbital period of days. The orbital light curve agrees with a model in which the modulation is caused by the changing aspect of the heated face of the secondary. The lack of eclipses rules out orbital inclinations . Our best models favor inclinations near and black hole masses near with a 90% upper bound of , and a lower bound of imposed solely by the maximum mass of neutron stars. We favor a black hole primary over a neutron star based on evidence from the X-ray spectra, the high spin of the compact object, and the lack of any observed type I X-ray bursts. Although uncertainties in the data allow for higher masses, the compact star in V1408 Aql is a candidate for a black hole lying in the mass gap.