In this paper, the event-triggered controller design method for the synchronization of chaotic neural networks (CNNs) is proposed by using clock-dependent Lyapunov functionals (CLF). The aim of this study is to propose the criterion for the event-triggered controller design which synchronizes two identical CNNs by using the sum of squares (SOS) programs. The synchronization criterion based on the event-triggered mechanism (ETM) is derived by using CLF which is a polynomial with respect to the piecewise-continuous delay defined as a clock. The derived condition is formulated as the SOS programs to obtain feasible solutions. The effectiveness of the proposed method is verified via the numerical simulation of the CNN.