No, there has never been a 27-strikeout baseball game. The all-time record for strikeouts in a 9-inning game is 20. This has been done by both Roger Clemens of the Boston Red Sox, and Kerry Wood of the Chicago Cubs.  It is worth noting that in 1962, Tom Cheney of the Washington Senators recorded 21 strikeouts in one game, but Cheney pitched 16 innings that game instead of just 9. The record for most strikeouts during a perfect game is 14 by Matt Cain of the San Francisco Giants on June 13, 2012.