  We report the discovery of a radio pulsar with a characteristic age of 7300
years, making it one of the 10 apparently youngest Galactic pulsars known. PSR
J1357-6429, with a spin period of P = 166 ms and spin-down luminosity of 3.1e36
ergs/s, was detected during the Parkes multibeam survey of the Galactic plane.
We have measured a large rotational glitch in this pulsar, with Delta P/P =
-2.4e-6, similar in magnitude to those experienced occasionally by the Vela
pulsar. At a nominal distance of only ~ 2.5 kpc, based on the measured free
electron column density of 127 pc/cc and the electron distribution model of
Cordes & Lazio, this may be, after the Crab, the nearest very young pulsar
known. The pulsar is located near the radio supernova remnant candidate
G309.8-2.6.
