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Triples are pretty fun. Usually, they happen for one of two reasons. The first is when a really fast guy gets a ball into the gap and speeds his way into third. The other is when a fielder royally messes up, and the defense can't clean up the mess until the batter is at third.
The record for triples in one game is four, and both happened a very long time ago. George Strief did it in 1885 in the American Association, and Bill Joyce did it in 1897. After that, there is a many-way tie for second place with three, a tie that includes the likes of Yasiel Puig, Willie Mays, and Baby Doll Jackson. Three Yankees are part of that tie for second. It was first accomplished back on August 30, 1906 by infamous first baseman Hal Chase in the second game of a doubleheader against the Washington Senators, but information on it is scarce since it predates Baseball-Reference Play Index logs. Fortunately, there is much more available on the other two record-tying days.
Earle Combs managed the feat on September 22, 1927, and it's not even remotely close to being the thing that is most remembered about that game. The Yankees won the game that day, scoring two runs in the ninth to turn around a 7-6 deficit. Those two runs in the ninth came on a Babe Ruth home run. It was his 56th of 60 for the season, on his way to breaking his own single season record. The Yankees also won their 105th game of the season, tying the 1912 Red Sox for the most wins in a season by an American League team.
Then there was Combs. He hit three triples that day, and somewhat amazingly, drove home no runs. He was the leadoff hitter and was hitting directly behind the pitcher, but still. The '27 Yankees were one of the greatest all-time offenses, but somehow no one was on base in each of the three times Combs hit a three-bagger. Combs led the league in triples that season with 23.
The other Yankee to accomplish the feat was another, more well known, Hall of Famer in Joe DiMaggio. His August 27, 1938 game was also overshadowed. Later that day, in game two of a doubleheader, Monte Pearson pitched a no-hitter for New York. No-hitters are something noted and treated as major accomplishments, but I'm more amazed by what DiMaggio did that day. The Yankees won the game on a walk-off. One of DiMaggio's triples was a two-run effort in the bottom of the ninth.
The aforementioned two games have a few similarities between them. Coincidentally, these games happened to finish with a score of 8-7, but more importantly, Lou Gehrig was the starting first baseman in both games, 11 years apart. It can take some randomness for even one triple to happen in a game. For that reason, I'm not sure if any Yankee will ever join Chase, Combs, and DiMaggio in replicating three triples in a game. We can dream, though.
Sources
http://www.baseball-almanac.com/recbooks/rb_trip1.shtml
http://www.baseball-reference.com/boxes/NYA/NYA192709220.shtml
http://www.baseball-reference.com/players/c/combsea01.shtml
http://www.baseball-reference.com/boxes/NYA/NYA193808271.shtml
http://www.baseball-reference.com/boxes/NYA/NYA193808272.shtml
http://www.nydailynews.com/archives/sports/day-yankee-history-article-1.513274
http://research.sabr.org/journals/three-triples (h/t YES Network's James Smyth)