Using soft x-ray observations of the bright new comet C/1999 S4 (LINEAR) with the Chandra x-ray observatory, we have detected x-ray line emission created by charge exchange between highly ionized solar wind minor ions and neutral gases in the comet's coma. The emission morphology was symmetrically crescent shaped and extended out to 300,000 kilometers from the nucleus. The emission spectrum contains 6 lines at 320, 400, 490, 560, 600, and 670 electron volts, attributable to electron capture and radiative deexcitation by the solar wind species C(+5), C(+6), N(+7), O(+7), and O(+8). A contemporaneous 7-day soft x-ray light curve obtained using the Extreme Ultraviolet Explorer demonstrates a large increase in the comet's emission coincident with a strong solar flare on 14 and 15 July 2000.