THE magnetic vortex lattice of copper oxide superconductors in the mixed (field-penetrated) state ’liquefies’(1,2) on increasing the temperature T or the external magnetic field H, giving rise to an ohmic resistivity well below the fluctuation-dominated crossover to the normal state at the upper critical field H-c2(T), Theoretical work suggests that in clean materials this melting is a first-order phase transition(3); features in the resistivity(4-6) and magnetization(7-10), as well as results from muon spin rotation(11) and neutron-diffraction work(12), have been cited to support this hypothesis, A calorimetric measurement of a latent heat provides the most definitive proof of the occurrence of a first-order transition, but such measurements require very high sensitivity, Here we report calorimetric measurements on an untwinned single crystal of YBa2Cu3O7-delta that have sufficient precision to clearly resolve the latent heat. The value obtained, similar to 0.45 k(B)T per vortex per superconducting layer (where k(B) is the Boltzmann constant), is consistent with that inferred from magnetization data using the Clapeyron equation, This result is compelling evidence for a first-order transition at a well defined phase boundary H-m(T).