The body of Matthew F. Norton, 55, chairman of the chemistry department at American University, was recovered Friday from the lower Chesapeake Bay, about one-half mile from where his sailboat was anchored.

The Coast Guard had begun searching for Norton Wednesday after the 20-foot sailboat was found unoccupied, its sails furled, in the bay about 35 miles north of Norfolk, between the James and Rappahannock rivers.

The scientist's body was recovered by the Coast Guard about 6 p.m. after being spotted by a passing pleasure boat. It was taken to the state medical examiner's office in Richmond and the cause of death could not be learned last night.However, a Coast Guard spokesman said there was no indication of foul play.

According to the Coast Guard, Norton, a Woodbridge, Va., resident set out Aug. 18 from Occoquan Bay, and reported the next day that he was heading for a marina in Mathews County, Va., and experiencing engine trouble. The sailboat had an outboard motor.

When his sailboat was found, the small boat it carried was missing, and it was speculated that he might have tried to use it to go ashore to obtain parts for repairs.

Norton, a New York native, held a Ph.D. in geology from Columbia University and had been on the AU faculty since 1958.

In 1966 he, his wife and their three children weathered a heavy squall on the Red Sea while on a projected 14-month round-the-world trip in a 72-foot schooner to study volcanoes.