A sudden depletion or intensity ``dimming'' of the X-ray corona sometimes accompanies a solar eruptive flare or coronal mass ejection (CME). We have identified a dimming that occurred just prior to a ``halo'' CME, observed on 1997 April 7 using the Soft X-ray Telescope (SXT) on Yohkoh. Halo CMEs are prime candidates for ``space weather'' effects. The dimming occurred in compact regions near a flare of 14 UT on April 7, over a projected area of about 1020 cm-2, and indicate that a mass of a few times 1014 g was ejected. This is a lower limit imposed by the obscuration of the dimming volume by the brightness of the accompanying flare and other factors. Most of the mass deficit comes from two regions close to the ends of a preflare S-shaped active-region structure, and the resulting dimmings in these regions persisted for more than three days following the flare. A cusp-shaped loop--not apparent prior to the flare--dominates the emission in the flare decay phase, and has a mass comparable to that lost in the dimming regions. Our findings are consistent with the source of the CME being a flux rope that erupted, leaving behind the dimming regions. The cusp-shaped loop probably represents magnetic fields reconfigured or reconnected by the eruption. We do not see an X-ray analog of the wavelike disturbance evident in SOHO EUV images.