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 +/- 0.4c, or 24.1 +/- 1.6 mas yr(-1), and in Knot D, with a speed of 2.4 +/- 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 similar to 420 mu G and similar to 230 mu 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.