On June 29, 1950 Harry Chiti was signed by the Chicago Cubs as an amateur free agent and became the youngest player in the National League when he made it into three games at age 17. After a couple more stays in Chicago while still a teenager and two years in the United States Army, he became a semi-regular behind the plate in Wrigley Field before being traded to the New York Yankees for veteran backup receiver, Charlie Silvera.

But Harry never made it into pinstripes and was drafted from the Yankees by the Kansas City Athletics in the 1957 Rule V Draft. After hitting in the .270 range for two seasons in Kansas City, he was sold to the Detroit Tigers on July 26, 1960. He was with the Tigers until July 21, 1961, did not play up to their expectations, and was traded to the Baltimore Orioles for Frank House.

The Orioles sent him to the Rochester Red Wings, their International League farm club and he hit .326 in 46 games. Baltimore then traded him, along with Ray Barker and Art Kay to the Cleveland Indians for Johnny Temple. On April 26, 1962 Harry was purchased by the New York Mets from the Indians for cash.

Chiti appeared in 15 games for the Mets, hitting .195 and was returned to the Indians in another cash transaction.

Harry Chiti is the only man in baseball history to be traded for himself. On April 26, 1962 he was acquired by the New York Mets, in their inaugural season, from the Cleveland Indians for a player to be named later. On June 15, 1962 he was named as the player to be named later and was returned to the Cleveland Indians, but never had an at-bat. This finished out his 10-season major league run. Harry appeared in 502 games, ending up with a career .238 batting average.

Harry spent the next two seasons in the International League (Jacksonville Florida AAA Cleveland Minors) and retired after the 1964 season with 13 active years in pro baseball. His minor league sheet shows he appeared in 608 games and had a career .271 batting average.

Chiti retired from baseball at age 30 to work as a district manager for Columbia Pictures, placing films in theaters. In the early 1970s he became a bailiff in the Shelby, Tennessee courthouse, before retiring in Winter Haven, FL. He died on January 31, 2002, at age 69 in Haines City, FL.

Harry's son Dom Chiti was a minor league pitcher who remained in the game as a major league coach.