Ultimate Tic-Tac-Toe is a variant of the well known tic-tac-toe (noughts and\ncrosses) board game. Two players compete to win three aligned "fields", each of\nthem being a tic-tac-toe game. Each move determines which field the next player\nmust play in.\n We show that there exist a winning strategy for the first player, and\ntherefore that there exist an optimal winning strategy taking at most 43 moves;\nthat the second player can hold on at least 29 rounds; and identify any optimal\nstrategy's first two moves.\n