Recent experiments on the interaction of intense, ultrafast laser pulses with large van der Waals bonded clusters have shown that these clusters can explode with substantial kinetic energy. By driving explosions in deuterium clusters with a 35 fs laser pulse, we have accelerated ions to sufficient kinetic energy to produce DD nuclear fusion. By diagnosing the fusion yield through measurements of 2.45 MeV fusion neutrons, we have found that the fusion yield from these exploding clusters varies strongly with the cluster size, consistent with acceleration of deuterons via Coulomb explosion forces.