  We present a deep observation with the X-ray Multi-Mirror Mission of PSR
B1823-13, a young pulsar with similar properties to the Vela pulsar. We detect
two components to the X-ray emission associated with PSR B1823-13: an elongated
core of extent 30'' immediately surrounding the pulsar, embedded in a fainter,
diffuse component of emission 5' in extent, seen only on the southern side of
the pulsar. The pulsar itself is not detected, either as a point source or
through its pulsations. Both components of the X-ray emission are well fit by a
power law spectrum, with photon index Gamma ~ 1.6 and X-ray luminosity (0.5-10
keV) L_x ~ 9e32 erg/s for the core, and Gamma ~ 2.3 and L_x ~ 3e33 erg/s for
the diffuse emission, for a distance of 4 kpc. We interpret both components of
emission as corresponding to a pulsar wind nebula, which we designate
G18.0-0.7. We argue that the core region represents the wind termination shock
of this nebula, while the diffuse component indicates the shocked downstream
wind. We propose that the asymmetric morphology of the diffuse emission with
respect to the pulsar is the result of a reverse shock from an associated
supernova remnant, which has compressed and distorted the pulsar-powered
nebula. Such an interaction might be typical for pulsars at this stage in their
evolution. The associated supernova remnant is not detected directly, most
likely being too faint to be seen in existing X-ray and radio observations.
