The dynamic back-action caused by electromagnetic forces (radiation pressure) in optical1, 2, 3, 4, 5, 6 and microwave7 cavities is of growing interest8. Back-action cooling, for example, is being pursued as a means of achieving the quantum ground state of macroscopic mechanical oscillators. Work in the optical domain has revolved around millimetre- or micrometre-scale structures using the radiation pressure force. By comparison, in microwave devices, low-loss superconducting structures have been used for gradient-force-mediated coupling to a nanomechanical oscillator of picogram mass7. Here we describe measurements of an optical system consisting of a pair of specially patterned nanoscale beams in which optical and mechanical energies are simultaneously localized to a cubic-micron-scale volume, and for which large per-photon optical gradient forces are realized. The resulting scale of the per-photon force and the mass of the structure enable the exploration of cavity optomechanical regimes in which, for example, the mechanical rigidity of the structure is dominantly provided by the internal light field itself. In addition to precision measurement and sensitive force detection9, nano-optomechanics may find application in reconfigurable and tunable photonic systems10, light-based radio-frequency communication11 and the generation of giant optical nonlinearities for wavelength conversion and optical buffering12