In this note we present an approximation algorithm for MAX 2SAT that given a (1 - epsilon) satisfiable instance finds an assignment of variables satisfying a 1 - O(sqrt{epsilon}) fraction of all constraints. This result is optimal assuming the Unique Games Conjecture.

The best previously known result, due to Zwick, was 1 - O(epsilon^{1/3}). We believe that the analysis of our algorithm is much simpler than the analysis of Zwick's algorithm.