Advancements in parallel and cluster computing have made many complex Monte Carlo simulations possible in the past several years. Unfortunately, cluster computers are large, expensive, and still not fast enough to make the Monte Carlo technique useful for calculations requiring a near real-time evaluation period. For Monte Carlo simulations, a small computational unit called a Field Programmable Gate Array (FPGA) is capable of bringing the power of a large cluster computer into any personal computer (PC). Because an FPGA is capable of executing Monte Carlo simulations with a high degree of parallelism, a simulation run on a large FPGA can be executed at a much higher rate than an equivalent simulation on a modern single-processor desktop PC. In this thesis, a simple radiation transport problem involving moderate energy photons incident on a three-dimensional target is discussed. By comparing the theoretical evaluation speed of this transport problem on a large FPGA to the evaluation speed of the same transport problem using standard computing techniques, it is shown that it is possible to accelerate Monte Carlo computations significantly using FPGAs. In fact, we have found that our simple photon transport test case can be evaluated in excess of 650 times faster on a large FPGA than on a 3.2 GHz Pentium-4 desktop PC running MCNP5—an acceleration factor that we predict will be largely preserved for most Monte Carlo simulations.