The feat of throwing the most consecutive no-hitters on record was achieved by Johnny Vander Meer on June 11, 1938, when he pitched a no-hitter against the Boston Bees. Just four days later, in the first night game ever played at Ebbets Field, he threw another no-hitter against the Brooklyn Dodgers, making him the only player in major league history to accomplish two consecutive no-hitters.
However, for someone to break this record, they would have to pitch three no-hitters in a row. Although it’s impossible to predict the future, this record seems unlikely to be broken anytime soon. Interestingly, Vander Meer witnessed his Cincinnati teammate Ewell Blackwell come close to matching his consecutive no-hit feat in 1947, by pitching a no-hitter against the Braves and holding the Dodgers without a hit until the ninth inning when he gave up two hits, thus only tying the record.