We have obtained initial spectroscopic observations and additional photometry of the newly discovered Pb = 94 minute γ-ray black-widow pulsar PSR J1311-3430. The Keck spectra show a He-dominated, nearly H-free photosphere and a large radial-velocity amplitude of 609.5 ± 7.5 km s-1. Simultaneous seven-color GROND photometry further probes the heating of this companion, and shows the presence of a flaring infrared excess. We have modeled the quiescent light curve, constraining the orbital inclination and masses. Simple heated light-curve fits give M NS = 2.7 M ☉, but show systematic light-curve differences. Adding extra components allows a larger mass range to be fit, but all viable solutions have M NS > 2.1 M ☉. If confirmed, such a large M NS substantially constrains the equation of state of matter at supernuclear densities.