ELECTRONS in a plasma undergo collective wave-like oscillations near the plasma frequency, These plasma waves can have a range of wavelengths and hence a range of phase velocities(1). Of particular note are relativistic plasma waves(2,3), for which the phase velocity approaches the speed of light; the longitudinal electric field associated with such waves can be extremely large, and can be used to accelerate electrons (either injected externally or supplied by the plasma) to high energies over very short distances(2-4). The maximum electric field, and hence maximum acceleration rate, that can be obtained in this way is determined by the maximum amplitude of oscillation that can be supported by the plasma(5-8). When this limit is reached, the plasma wave is said to ’break’. Here we report observations of relativistic plasma waves driven to breaking point by the Raman forward-scattering instability(9,10) induced by short, high-intensity laser pulses, The onset of wave-breaking is indicated by a sudden increase in both the number and maximum energy (up to 44 MeV) of accelerated plasma electrons, as well as by the loss of coherence of laser light scattered from the plasma wave.