Pulse arrival time measurements have been obtained over a 2 year inter
val for PSR J0437-4715 using the Parkes radio telescope. These data sh
ow that the proper motion of the pulsar is 135 +/- 4 mas yr(-1) at a p
osition angle of 122 degrees +/- 2 degrees. This agrees well with the
proper motion of the optical companion, putting the association beyond
doubt. An H alpha image confirms that the nebulosity first detected b
y Bell, Bailes, and Bessell is a bow shock associated with the pulsar
and shows that its orientation is close to that expected from the prop
er motion.