In Aachen, West Germany, Gail Greenough reeled off four faultless rounds to become both the first Canadian and first woman to win the world championship.

Greenough, 26, a decided outsider who was pitted against three of the world's most successful show riders, won without drawing one penalty point.

Conrad Homfeld of the United States, who won the 1984 Olympic silver medal, took the silver with a total of eight penalty points. Nick Skelton of Britain won the bronze medal on 10 fault points, all incurred in handling problems with Greenough's horse, Mr. T.

Pierre Durand of France, who had led the field after the three qualifying legs earlier this week, struggled on all four horses in the final and ended fourth on 32 points . . .

Box Car Willie, ridden by Rodney Jenkins of Orange, Va., won the $50,000 U.S. Grand Prix League Virginia Governor's Cup Show Jumping at Commonwealth Park in Culpeper in 39.030 seconds. Jenkins now leads the U.S. Grand Prix League in money won and points in the 1986 season. Dutch Crown, ridden by Harry DeLeyer of East Hampton, N.Y., finished second in 39.729. and V.I.P., ridden by Steve Stephens of Ambler, Pa., was third in 43.726.