We use data from the Advanced CCD Imaging Spectrometer (ACIS) on the Chandr
a X-Ray Observatory to image the shell surrounding the pulsar B0540-69.3 an
d measure its spectral properties. Weak emission-line features, notably of
Fe, Mg, and Si, indicate that the shell is composed primarily of ambient ma
terial heated by the blast wave. The shell emission in the east is faint an
d circular in appearance, with a temperature and ionization age of approxim
ately 5 keV and 10(10) cm(-3) s, respectively. The emission in the west is
brighter and has a more complex, distorted morphology and is fitted with si
gnificantly lower average temperatures and higher ionization ages. An image
with photon energies above 2 keV shows two hard arcs of emission located d
iametrically opposite each other at the outer boundary of the remnant shell
; the spectra from these regions could include a substantial nonthermal com
ponent.