The young pulsar PSR B0540-69 was one of the first targets observed with th
e 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. = 05(h)40(m)11(s).221, decl. = -69 deg
rees 19'54." 98 (J2000) with a 1 sigma radial uncertainty 0."7. Combining o
ur measurements of the pulsar period with previous measurements covering a
span of 12 years, we derive a braking index of 2.082 +/- 0.005 (95% confide
nce). The spectrum of the pulsed emission is consistent with a power law wi
th a photon index of 1.83 +/- 0.13. The compact nebula has a softer spectru
m with a photon index of 1.85-2.26.