When liquid (4)He is cooled below 2.176 K, it undergoes a phase transition-Bose-Einstein condensation-and becomes a superfluid with zero viscosity. Once in such a state, it can flow without dissipation even through pores of atomic dimensions. Although it is intuitive to associate superflow only with the liquid phase, it has been proposed theoretically that superflow can also occur in the solid phase of (4)He. Owing to quantum mechanical fluctuations, delocalized vacancies and defects are expected to be present in crystalline solid (4)He, even in the limit of zero temperature. These zero-point vacancies can in principle allow the appearance of superfluidity in the solid. However, in spite of many attempts, such a 'supersolid' phase has yet to be observed in bulk solid (4)He. Here we report torsional oscillator measurements on solid helium confined in a porous medium, a configuration that is likely to be more heavily populated with vacancies than bulk helium. We find an abrupt drop in the rotational inertia of the confined solid below a certain critical temperature. The most likely interpretation of the inertia drop is entry into the supersolid phase. If confirmed, our results show that all three states of matter-gas, liquid and solid-can undergo Bose-Einstein condensation.