The hierarchical triple system PSR J0337+1715 offers an unprecedented laboratory to study secular evolution of interacting systems and to explore the complicated mass-transfer history that forms millisecond pulsars and helium-core white dwarfs. The latter in particular, however, requires knowledge of the properties of the individual components of the system. Here we present precise optical spectroscopy of the inner companion in the PSR J0337+1715 system. We confirm it as a hot, low-gravity DA white dwarf with Teff=15,800+/-100 K and log(g)=5.82+/-0.05. We also measure an inner mass ratio of 0.1364+/-0.0015, entirely consistent with that inferred from pulsar timing, and a systemic radial velocity of 29.7+/-0.3 km/s. Combined with the mass (0.19751 Msun) determined from pulsar timing, our measurement of the surface gravity implies a radius of 0.091+/-0.005 Rsun; combined further with the effective temperature and extinction, the photometry implies a distance of 1300+/-80 pc. The high temperature of the companion is somewhat puzzling: with current models, it likely requires a recent period of unstable hydrogen burning, and suggests a surprisingly short lifetime for objects at this phase in their evolution. We discuss the implications of these measurements in the context of understanding the PSR J0337+1715 system, as well as of low-mass white dwarfs in general. ; Comment: ApJ Letters, in press. 6 pages, two figures. v2 fixes typo