This paper deals with the global asymptotic synchronization problem for a class of chaotic neural networks with delay. Using the drive-response conception and linear matrix inequality technique, two sufficient conditions are derived to guarantee the global synchronization of two chaotic neural networks with identical structure and different initial conditions, which also present a procedure to construct a synchronization controller. The controller gain can be achieved by solving a linear matrix inequality, and therefore, it is easily implemented in practice. Two illustrative examples are used to demonstrate the effectiveness of the proposed method.