"pool of money in a card game," 1884, American English, of uncertain origin. OED connects it with kit (n.1) in the 19c. sense of "collection of necessary supplies;" but perhaps it is rather from northern England slang kitty "prison, jail, lock-up" (1825), a word itself of uncertain origin.
By the Widow, or as it is more commonly known as "Kitty," is meant a percentage, taken in chips at certain occasions during the game of Poker. This percentage may be put to the account of the club where the game is being played, and defrays the cost of cards, use of chips, gas, attendance, etc. The Kitty may, however, be introduced when no expenses occur. ["The Standard Hoyle," New York, 1887]