ALTHOUGH gamma-ray bursters (GRBs) have been known for more than 20 years, no source has ever been identified in its quiescent state which might provide clues to its nature. On the other hand, two of the three known soft gamma-ray repeaters (SGRs), which emit intermittent bursts of soft gamma-rays. seem to be associated with supernova remnants1,2, and the recent identification of X-rays from one of these, SGR1806 - 20, supports the suggestion that a pulsar inside the remnant is the source of the gamma-rays3-5. Here we report X-ray observations of SGR0525 - 66, which has been associated previously with the supernova remnant N49 (ref. 1). We identify point-like emission from a source coincident with SGR0525 - 66, which suggests that it too is a pulsar. The pulsar seems to be only about 5,000 years old and has a high transverse velocity of about 1,200 km s-1, and we predict that the plerion (the region of radio synchrotron emission surrounding the pulsar) will be between 0.1 and 0.3 arcsec across. A high birth velocity has been estimated for the pulsar associated with SGR1806 - 20 also4, and this characteristic may be related to the reason why only a very few pulsars become SGRs.