We report on the results of spectral fits made to a NuSTAR observation of the black hole GRS 1915+105 in a “plateau” state. This state is of special interest because it is similar to the “low/hard” state seen in other black holes, especially in that compact, steady jets are launched in this phase. The 3-79 keV bandpass of NuSTAR , and its ability to obtain moderate-resolution spectra free from distortions such as photon pile-up, are extremely well suited to studies of disk reflection in X-ray binaries. In only 15 ks of net exposure, an extraordinarily sensitive spectrum of GRS 1915+105 was measured across the full bandpass. Ionized reflection from a disk around a rapidly spinning black hole is clearly required to fit the spectra; even hybrid Comptonization models including ionized reflection from a disk around a Schwarzschild black hole proved inadequate. A spin parameter of a = 0.98 ± 0.01 (1σ statistical error) is measured via the best-fit model; low spins are ruled out at a high level of confidence. This result suggests that jets can be launched from a disk extending to the innermost stable circular orbit. A very steep inner disk emissivity profile is also measured, consistent with models of compact coronae above Kerr black holes. These results support an emerging association between the hard X-ray corona and the base of the relativistic jet.