The first stars are the key to the formation of primitive galaxies, early cosmological reionization and chemical enrichment, and the origin of supermassive black holes. Unfortunately, in spite of their extreme luminosities, individual Population III stars will likely remain beyond the reach of direct observation for decades to come. However, their properties could be revealed by their supernova explosions, which may soon be detected by a new generation of NIR observatories such as JWST and WFIRST. We present light curves and spectra for Pop III pair-instability supernovae calculated with the Los Alamos radiation hydrodynamics code RAGE. Our numerical simulations account for the interaction of the blast with realistic circumstellar envelopes, the opacity of the envelope, and Lyman absorption by the neutral IGM at high redshift, all of which are crucial to computing the NIR signatures of the first cosmic explosions. We find that JWST will detect pair-instability supernovae out to z > 30, WFIRST will detect them in all-sky surveys out to z ~ 15 - 20 and LSST and Pan-STARRS will find them at z ~ 7 - 8. The discovery of these ancient explosions will probe the first stellar populations and reveal the existence of primitive galaxies that might not otherwise have been detected.