THE peculiar fan-shaped morphology of the galactic radio source G5.4-1.2 has prompted much speculation about its nature 1-4. Here we report high-resolution observations obtained with the Very Large Array, which reveal a compact, highly polarized, flat-spectrum radio nebula on the western edge of G5.4-1.2. We also confirm the presence of a 125-ms pulsar 5, PSR1757-24, associated with the radio source, and find that it is located near the centre of the newly discovered nebula. We argue that the pulsar is associated with G5.4-1.2, which we identify as a supernova remnant, and that it was born with a high enough velocity, approximately 2,000 km s-1, for it to overtake the decelerating supernova shell, creating the peripheral radio nebula. The fortuitous near-coincidence of the pulsar velocity with the shell velocity accounts for the unusual overall shape of the remnant. If the large velocity of the pulsar is confirmed by future observation of its proper motion, the possibility of asymmetric supernova explosions must be taken seriously, and other previously unsuspected associations between pulsars and supernova remnants may emerge.