Nobody knows. Apparently that record was never kept, and it is now near impossible to go back and determine what the record is or who holds it. One possibility is Joe DiMaggio, in that famous 1941 season. Everyone knows about the 56-game hitting streak, but what is less well known is that after the streak was broken on July 17, 1941 (though he did draw a walk), Joltin’ Joe immediately followed with a 16-game hitting streak. So if not for sterling defensive plays by Indians third baseman Ken Keltner and shortstop Lou Boudreau, the Yankee Clipper might have had a 73-game hitting streak. Even so, the walk allowed his streak of reaching base safely to continue, and eventually reach 73 games. However, this is just one possibility. Would it surprise anyone if Ted Williams, with his career .483 OBP, managed a longer streak at some point during his career?