While progress in fusion research continues with magnetic and inertial confinement, alternative approaches--such as Coulomb explosions of deuterium clusters and ultrafast laser-plasma interactions--also provide insight into basic processes and technological applications. However, attempts to produce fusion in a room temperature solid-state setting, including 'cold' fusion and 'bubble' fusion, have met with deep scepticism. Here we report that gently heating a pyroelectric crystal in a deuterated atmosphere can generate fusion under desktop conditions. The electrostatic field of the crystal is used to generate and accelerate a deuteron beam (> 100 keV and >4 nA), which, upon striking a deuterated target, produces a neutron flux over 400 times the background level. The presence of neutrons from the reaction D + D --> 3He (820 keV) + n (2.45 MeV) within the target is confirmed by pulse shape analysis and proton recoil spectroscopy. As further evidence for this fusion reaction, we use a novel time-of-flight technique to demonstrate the delayed coincidence between the outgoing alpha-particle and the neutron. Although the reported fusion is not useful in the power-producing sense, we anticipate that the system will find application as a simple palm-sized neutron generator.