Periodicity in materials yields interesting and useful phenomena. Applied to the propagation of light, periodicity gives rise to photonic crystals, which can be precisely engineered for such applications as guiding and dispersing optical beams, tightly confining and trapping light resonantly, and enhancing nonlinear optical interactions. Photonic crystals can also be formed into planar lightwave circuits for the integration of optical and electrical microsystems. In a photonic crystal, the periodicity of the host medium is used to manipulate the properties of light, whereas a phononic crystal uses periodicity to manipulate mechanical vibrations. As has been demonstrated in studies of Raman-like scattering in epitaxially grown vertical cavity structures and photonic crystal fibres, the simultaneous confinement of mechanical and optical modes in periodic structures can lead to greatly enhanced light-matter interactions. A logical next step is thus to create planar circuits that act as both photonic and phononic crystals: optomechanical crystals. Here we describe the design, fabrication and characterization of a planar, silicon-chip-based optomechanical crystal capable of co-localizing and strongly coupling 200-terahertz photons and 2-gigahertz phonons. These planar optomechanical crystals bring the powerful techniques of optics and photonic crystals to bear on phononic crystals, providing exquisitely sensitive (near quantum-limited), optical measurements of mechanical vibrations, while simultaneously providing strong nonlinear interactions for optics in a large and technologically relevant range of frequencies.