There was a guy name Greg Harris who sometimes pitched both lefty and righty in the same at-bat. This so disconcerted hitters that MLB ruled that a pitcher could not pitch from both sides in the same at bat, although it is OK to change with each batter. Harris spent much of his career with the Expos.

On September 28, 1995: The Reds defeat the Expos by a score of 9-7, with Expos reliever Greg Harris pitching the 9th ambidexterously. The Reds don't score against him as he faces two with his (normal) right arm and two with his left. After Harris (right-handed) retires Reggie Sanders on a grounder, manager Felipe Alou permits him to do what he had wanted to try for 10 years. Following a wild lefty toss to the backstop, he walks Hal Morris. Remaining as a southpaw, though, he gets Eddy Taubensee to ground out. Finally, returning the ball to his right hand, he retires Bret Boone on a ground out. Harris uses a special six-finger glove, which is sent to the Hall of Fame. Before Harris, Bert Campaneris was the last pitcher to use both hands in a professional game, doing it in 1962 for Daytona Beach in the Florida State League. The only major leaguers to toss with each hand are: Tony Mullane (July 18, 1882); Larry Corcoran (June 10, 1884); Elton "Icebox" Chamberlain (May 9, 1888); Tony Mullane again (July 14, 1893).

http://www.baseballlibrary.com/.../Harris_Greg.stm

Greg Harris, but he only did it once, in the ninth inning, as an Expo, against the Reds on September 28, 1995.