  Chandra HRC observations are investigated for evidence of proper motion and
brightness changes in the X-ray jet of the nearby radio galaxy M87. Using
images spanning 5 yr, proper motion is measured in the X-ray knot HST-1, with a
superluminal apparent speed of $6.3 \pm 0.4 c$, or $24.1 \pm 1.6\rm\ mas\
yr^{-1}$, and in Knot D, with a speed of $2.4\pm 0.6c$. Upper limits are placed
on the speeds of the remaining jet features. The X-ray knot speeds are in
excellent agreement with existing measurements in the radio, optical, and
ultraviolet. Comparing the X-ray results with images from the Hubble Space
Telescope indicates that the X-ray and optical/UV emitting regions co-move. The
X-ray knots also vary by up to 73% in brightness, whereas there is no evidence
of brightness changes in the optical/UV. Using the synchrotron cooling models,
we determine lower limits on magnetic field strengths of $\sim 420~\mu \rm G$
and $\sim 230~\mu \rm G$ for HST-1 and Knot A, respectively, consistent with
estimates of the equipartition fields. Together, these results lend strong
support to the synchrotron cooling model for Knot HST-1, which requires that
its superluminal motion reflects the speed of the relativistic bulk flow in the
jet.
