This paper discusses the implementation of Hopfield neural networks for solving constraint satisfaction problems using field programmable gate arrays (FPGAs). It discusses techniques for formulating such problems as discrete neural networks, and then it describes the N-Queen problem using this formulation. Finally results will be presented which compare the computation times for the custom computer against the simulation of the Hopfield network run on a high end workstation. In this way, the speed-up can be determined, that illustrate a speedup of up to 2 to 3 orders of magnitude is possible using current FPGAs devices. Key words: Hopfield neural network, field programmable gate arrays (FPGA), N-Queen problem.