We report on a unique observation of the early and rapid acceleration of a fast CME in the low solar corona. The coronal disturbance associated with a LASCO CME and concurrent X1.2 flare on 1998 April 23 was well-observed by the Yohkoh Soft X-ray Telescope. The X-ray observations clearly show an accelerating structure, reaching 800--1100 km/s in ~500s at a de-projected height of only 280 Mm, indicating an acceleration well in excess of 1700 m/s2. The soft X-ray observations are coincident with the onset of the CME, which ultimately attained a velocity of 1390 km/s and generated a number of interplanetary radio signatures, frequently associated with fast events. Assuming a constant acceleration, a0, throughout the duration of the X-ray observations, we determine a best-fit value of a0 = 1756 m/s2, while application of a power-law acceleration model yields a better fit to the data with a peak acceleration of ~4865 m/s2 within the first 280 Mm of the solar corona.