Stochastic resonance is a counterintuitive concept: the addition of noise to a noisy system induces coherent amplification of its response. First suggested as a mechanism for the cyclic recurrence of ice ages, stochastic resonance has been seen in a wide variety of macroscopic physical systems: bistable ring lasers, superconducting quantum interference devices (SQUIDs), magnetoelastic ribbons and neurophysiological systems such as the receptors in crickets and crayfish. Although fundamentally important as a mechanism of coherent signal amplification, stochastic resonance has yet to be observed in nanoscale systems. Here we report the observation of stochastic resonance in bistable nanomechanical silicon oscillators. Our nanomechanical systems consist of beams that are clamped at each end and driven into transverse oscillation with the use of a radiofrequency source. Modulation of the source induces controllable switching of the beams between two stable, distinct states. We observe that the addition of white noise causes a marked amplification of the signal strength. Stochastic resonance in nanomechanical systems could have a function in the realization of controllable high-speed nanomechanical memory cells, and paves the way for exploring macroscopic quantum coherence and tunnelling.