  The young pulsar PSR B0540-69 was one of the first targets observed with the
Chandra X-Ray Observatory. The high angular resolution of Chandra allows us to
resolve the compact nebula surrounding the pulsar. We have determined a
position for PSR B0540-69 of R.A. = 05h 40m 11s.221, decl. = -69o 19' 54".98
(J2000) with a 1-sigma radial uncertainty of 0.7". Combining our measurements
of the pulsar period with previous measurements covering a span of 12 years, we
derive a braking index of 2.08. The spectrum of the pulsed emission is
consistent with a power-law with a photon index of 1.83 +/- 0.13. The compact
nebula has a softer spectrum with a photon index of 1.85 to 2.26.
