  We report the discovery of PSR J1747-2958, a radio pulsar with period P = 98
ms and dispersion measure DM = 101 pc/cc, in a deep observation with the Parkes
telescope of the axially-symmetric "Mouse" radio nebula (G359.23-0.82). Timing
measurements of the newly discovered pulsar reveal a characteristic age Pdt/2dP
= 25 kyr and spin-down luminosity dE/dt = 2.5e36 erg/s. The pulsar (timing)
position is consistent with that of the Mouse's "head". The distance derived
from the DM, ~2 kpc, is consistent with the Mouse's distance limit from HI
absorption, < 5.5 kpc. Also, the X-ray energetics of the Mouse are compatible
with being powered by the pulsar. Therefore we argue that PSR J1747-2958,
moving at supersonic speed through the local interstellar medium, powers this
unusual non-thermal nebula. The pulsar is a weak radio source, with
period-averaged flux density at 1374 MHz of 0.25 mJy and luminosity ~1 mJy
kpc^2.
