The faint radio supernova remnant SNR G315.9-0.0 is notable for a long and thin trail that extends outward perpendicular from the edge of its approximately circular shell. In a search with the Parkes telescope, we have found a young and energetic pulsar that is located at the tip of this collimated linear structure. PSR J1437-5959 has period P = 61 ms, characteristic age kyr, and spin-down luminosity ergs-1. It is very faint, with a flux density at 1.4GHz of about 75 μJy. From its dispersion measure of 549pccm-3, we infer d 8kpc. At this distance and for an age comparable to τc, the implied pulsar velocity in the plane of the sky is V t = 300kms-1 for a birth at the center of the SNR, although it is possible that the SNR/pulsar system is younger than τc and that Vt > 300kms-1. The highly collimated linear feature is evidently the pulsar wind trail left from the supersonic passage of PSR J1437-5959 through the interstellar medium surrounding SNR G315.9-0.0.