We have used NIRSPEC on Keck II to obtain K-band spectroscopy of the low-mass X-ray binary V616 Mon (=A0620-00). V616 Mon is the prototypical soft X-ray transient containing a black hole primary. As such it is important to constrain the masses of the binary components. The modeling of the infrared observations of ellipsoidal variations in this system lead to a derived mass of 11.0 Msolar for the black hole. The validity of this derivation has been called into question due to the possibility that the secondary star's spectral energy distribution is contaminated by accretion disk emission (acting to dilute the variations). Our new K-band spectrum of V616 Mon reveals a late-type K dwarf secondary star, but one that has very weak 12CO absorption features. Comparison of V616 Mon with SS Cyg leads us to estimate that the accretion disk supplies only a small amount of K-band flux, and the ellipsoidal variations are not seriously contaminated. If true, the derived orbital inclination of V616 Mon is not greatly altered, and the mass of the black hole remains large. A preliminary stellar atmosphere model for the K-band spectrum of V616 Mon reveals that the carbon abundance is approximately 50% of the solar value. We conclude that the secondary star in V616 Mon has either suffered serious contamination from the accretion of supernova ejecta that created the black hole primary or is the stripped remains of a formerly more massive secondary star, one in which the CNO cycle had been active.