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We propose a chaotic neural network to solve the graph coloring problem, which is a classic NP-complete graph optimization problem. Since the graph coloring problem is consistent with the channel routing problem, a prominent problem in the physical design of VLSI chips, algorithms that can solve the graph coloring problem well can, inevitably, solve the channel routing problem effectively. From some detailed analyses, we reach the conclusion that, unlike the conventional Hopfield neural networks for the graph coloring problem, the chaotic neural network can avoid getting stuck into local minima and thus yields excellent solutions. Experimental results verify that the chaotic neural network provides a more effective approach than many other heuristic algorithms for the graph coloring problem, and thus has a profound application potential in VLSI channel routing.