A high-velocity coronal mass ejection (CME) associated with the 2002 April 21 X1.5 flare is studied using a unique set of observations from the Transition Region and Coronal Explorer ( TRACE), the Ultraviolet Coronagraph Spectrometer (UVCS), and the Large Angle and Spectroscopic Coronagraph (LASCO). The event is first observed as a rapid rise in GOES X-rays, followed by two simultaneous brightenings that appear to be connected by an ascending looplike feature. While expanding, the appearance of the feature remains remarkably constant as it passes through the TRACE 195 Angstrom passband and LASCO fields of view, allowing its height-time behavior to be accurately determined. The acceleration is consistent with an exponential rise with an e-folding time of similar to138 s and peaks at similar to1500 m s(-2) when the leading edge is at similar to1.7 R., from Sun center. The acceleration subsequently falls off with an e-folding time of over 1000 s. At distances beyond similar to3.4 R., the height-time profile is approximately linear with a constant velocity of similar to2500 km s(-1). These results are briefly discussed in light of recent kinematic models of CMEs.