THE observable interactions of neutron stars with their local environment provide an opportunity for measuring the properties of both relativistic pulsar winds and the surrounding interstellar medium. Here we report the discovery of a prominent nebula produced by the motion of a high-velocity pulsar, PSR 2224 + 65, through partially neutral gas. The pulsar's transverse speed of >== 800 km s-1 makes it arguably the fastest known star in the Galaxy and guarantees that it will ultimately escape the galactic potential well. A deep Hα image reveals a bright head and a faint, limb-brightened 'body' whose variable width suggests that the ambient interstellar gas has density variations on length scales <==0.1 pc. Thermalization of shock energy occurs at a rate of about 10-2 times the pulsar's spindown loss rate. Our observations provide some insights into the likelihood of finding shocks around other pulsars and the use of nebulae to find high-velocity neutron stars either not acting as pulsars or with their radiation beamed away from the Earth.