Magnetic reconnection, the process by which magnetic lines of force break and rejoin into a lower-energy configuration, is considered to be the fundamental process by which magnetic energy is converted into plasma kinetic energy(1). The Sun has a large reservoir of magnetic energy, and the energy released by magnetic reconnection has been invoked to explain both large-scale events, such as solar flares(2,3) and coronal mass ejections(4), and small-scale phenomena, such as the coronal and chromospheric microflares that probably heat and accelerate the solar wind(5,6). But the observational evidence for reconnection is largely indirect, resting on observations of variations in solar X-ray morphology and sudden changes in the magnetic topology(7,8), and on the apparent association between some small-scale dynamic events and magnetic bipoles(9,10). Here we report ultraviolet observations of explosive events in the solar chromosophere that reveal the presence of bi-directional plasma jets ejected from small sites above the solar surface. The structure of these jets evolves in the manner predicted by theoretical models of magnetic reconnection(11,12), thereby lending strong support to the view that reconnection is the fundamental process for accelerating plasma on the Sun.