This is actually two games, and there's a specific reason for that. On May 30, 1922, the Cubs and Cardinals played a Memorial Day doubleheader at Cubs Park. The Cubs began the day slightly under .500 (18-20); the Cardinals slightly over (23-18).
It's what happened between the two games that's of interest to us on this date. The Tribune has the story:
Between the morning and afternoon games of the Cubs holiday bill yesterday, Managers Bill Killefer of the locals and Branch Rickey of the Cardinals got together and arranged an even trade of Max Flack, Cubs outfielder, and Cliff Heathcote, St. Louis gardener. No money was involved. The trade took effect at once, Flack playing with St. Louis and Heathcote with Chicago in the afternoon. Flack started his career in organized ball with the Peoria club and came to the Chicago club in the Federal league in 1914. Flack joined the Cubs when that team absorbed the Feds. Heathcote was secured by the Cards in 1918, coming from Penn State university where he was one of the stars of the freshman and varsity nines. He had no previous experience in league ball.
That article isn't quite right -- Heathcote played 20 games for a minor-league team in Houston in 1918 before coming to St. Louis, but that was his only professional experience outside the majors. Branch Rickey, later the general manager who brought Jackie Robinson to the Dodgers to break the color barrier, was Cardinals field manager from 1918-1925. You'll note that in that era, field managers made trades -- general managers, if teams even had a man with that title (most didn't until the 1930s), were more like the head of the business side of a team today.
The trade was better for the Cubs; Flack had been a pretty good player for the Cubs, but Heathcote was eight years younger. He played for the Cubs through 1930, and was part of the 1929 Cubs N.L. champions, although by then he was a backup. Flack was out of the majors by 1926. Heathcote is the player pictured at the top of this post.
On that May 30 date, the Cubs swept the doubleheader, 4-1 and 3-1. Flack went 0-for-4 (with one RBI) for the Cubs in game 1, while Heathcote was going 0-for-3 for the Cardinals; after they switched clubhouses and uniforms, Heathcote went 2-for-4 for the Cubs in the nightcap, while Flack went 1-for-4.
It's the only time in major-league history such a deal has been consummated; the only other time a player has played for two teams in one day was August 4, 1982, and that also involved the Cubs, though they weren't involved in the trade.
Mets outfielder Joel Youngblood started this afternoon game at Wrigley Field and was pulled in the fourth inning when he was traded to the Expos for a PTBNL (Montreal later sent pitcher Tom Gorman to the Mets). The Expos put him on a plane to Philadelphia, where they were playing that night. He arrived in time to be inserted in the lineup in this game; he later singled. He's the only player in baseball history to play for two different teams in two different cities on the same day.