This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to develop thinking strategies. Chess is a game that serves both functions simultaneously in that it involves numerous calculations--comparative value of pieces, number of squares that can be moved, the patterns in which they move, as well as higher-order thinking involving prediction, planning, and analysis. The "Chess Effect" works on numerous levels lasting a lifetime. (Contains 8 figures.)