We present the first ever calculations of the neutrino signal from pair-instability supernovae (PISNe) using two hydrodynamical simulations which bracket the mass range of the stars which explode via this mechanism. We take into account both the time and energy dependence of the emission and the flavor oscillations, as well as investigating the equation-of-state dependence. We then process the computed neutrino fluxes at Earth through four different neutrino detectors. We show how the neutrino signal from PISNe possesses unique features that distinguish it from other supernovae, how the detectors we consider are capable of observing neutrinos from PISNe at the standard distance of 10 kpc, and how the proposed HyperKamiokande detector can even reach the Large Magellanic Cloud and the several very high mass stars known to exist there.