For 3,914 games, the Oakland Athletics have recorded at least one hit in every regular season game they've played, but there have been a few close calls in the 25 years since.
It's been 3,914 regular season games since the Oakland Athletics recorded no hits against Baltimore Orioles pitchers Bob Milacki, Mike Flanagan, Mark Williamson, and Gregg Olson on July 13, 1991. Now that the Cincinnati Reds failed to record a hit against Chicago Cubs ace Jake Arrieta on Thursday, it's now the longest active no no-hit streak in MLB (visualization from Scott Lindholm as of the end of April 21):
If you click the "All-Time" tab on that chart, you'll see that the A's are probably a little over 10 years away from the American League record of 5,550 games held by the 1973-2008 Kansas City Royals, and just under 25 years away from the MLB record of 7,920 games owned by the 1965-2015 Chicago Cubs.