We quantize the game of tic-tac-toe, by allowing superpositions of classical moves. To play the game, we require quantum moves so defined to be orthogonal to all previous moves, and to compute the weight a player has at a given site, we square the sum of the amplitudes at this site over all his moves. A player wins when the sum of weights along any of the eight straight lines we can draw in the 3 x 3 grid is greater than 3. We play the quantum tic-tac-toe first randomly, and then deterministically, to explore the impacts different opening moves, end games, and blocking strategies have on the outcome of the game. In contrast to the classical game of tic-tac-toe, the deterministic quantum game do not always end up in a draw, and do not always favour the starting player.