The acceleration of electrons to approximately 0.8 GeV has been observed in a self-injecting laser wakefield accelerator driven at a plasma density of 5.5x10(18) cm(-3) by a 10 J, 55 fs, 800 nm laser pulse in the blowout regime. The laser pulse is found to be self-guided for 1 cm (>10zR), by measurement of a single filament containing >30% of the initial laser energy at this distance. Three-dimensional particle in cell simulations show that the intensity within the guided filament is amplified beyond its initial focused value to a normalized vector potential of a0>6, thus driving a highly nonlinear plasma wave.