About 30 km of 600 MeV positron tracks have been followed in a propane bubble chamber operating in a magnetic field. 575 positron-electron annihilation events were observed giving, after corrections, a cross-section of 1.563 mb±4.5%. The experimental corrections are small and are described in detail. The result is compared with the calculation of lowest-order quantum electrodynamics. The ratioσexp/σth. lowest order = 1.085±0.047. This ratio together with those obtained from other experiments are compared to theoretical predictions of deviations from the lowest-order calculation due to radiative corrections and due to possible failures in quantum electrodynamics.