On April 19, 1991, Atlanta Hawks big man Moses Malone played in his 1,046th game without fouling out in a 126-120 loss to the Pistons in Detroit. The milestone set a new NBA record that had been held by Wilt Chamberlain. The last time Malone fouled out of a game was in 1978 when he was a member of the Houston Rockets. He then went on a streak that has been matched by no other, by playing the final 1,212 games of his career without fouling out.
You can read about the life and Hall of Fame career of Moses Malone here: