The Athletics only gave up one player, sending Rocky Colavito to the Indians.
It's easy to assume that Colavito was the biggest name in this deal, since Kansas City got 3 players in return for one. The Chisox gave up 4 players to get 3, while the Indians gave up 3 players to get two.
Although Colavito was the biggest name at the time, Tommy John was the long-term star, playing an additional TWENTY-FOUR seasons for the White Sox, Dodgers, Yankees, and Angels. Tommie Agee was a starting outfielder for the White Sox and Mets from 1966-1973, and starred in the 1969 World Series for the Mets. John Romano was Chicago's starting catcher in '65 and '66, before wrapping up his career in 1967 as a reserve with the Cardinals.
The Indians and Athletics didn't fare as well in this deal:
Colavito was washed up by the end of 1966, and finished his career bouncing to the White Sox, Dodgers, and Yankees from 1967-69. Camilo Carreon spent most of '65 and '66, and all of 1967 in the minors before retiring.
Longtime White Sox' center fielder Jim Landis was an A's regular in 1965, then spent 1966 in Cleveland before ending his career in 1967 with several teams. Mike Hershberger played several seasons with the A's before returning to the White Sox for his final season in 1971. Fred Talbot pitched briefly for Kansas City, before moving to the Yankees for several seasons, and popping up on the Seattle Pilots in 1969 (much to Jim Bouton's dismay).