On April 21, 1997, about 1700 eastern daylight time, the captain of a British Aerospace (BAE) 125-800A, N900KC, became incapacitated during cruise flight, enroute to Dekalb-Peachtree Airport, Atlanta, Georgia. The airplane was operated by Kimberly Clark Corporation under the provisions of Title 14 CFR Part 91, and instrument flight rules. An instrument flight plan was filed for the corporate flight. Visual flight conditions prevailed. The airline transport pilot captain was incapacitated, and the airline transport pilot second-in-command was not injured. There was no damage to the airplane. Origination of the flight was Oxford, Connecticut, about 1630 on the same day. According to the captain, during cruise flight at FL 390, he started experiencing "mild stomach pain accompanied by some feverishness." When the flight was over the vicinity of Asheville, North Carolina, about 35 minutes from Peachtree Airport, he was unable to continue his cockpit duties, and went to the passenger cabin. The second-in-command continued the flight to the destination, since the descent profile to their home base placed it as close as any suitable divert location, and he was more familiar with the approach. An uneventful landing was made by the second pilot. Emergency personnel transported the captain to the hospital where he was treated for kidney stones.