In this paper, we discuss the implementation of a lattice Quantum Chromodynamics (QCD) application to a Xilinx VirtexII FPGA device on an Alpha Data ADM-XRC-II board using Handel-C and logarithmic arithmetic. The specific algorithm implemented is the Wilson Dirac Fermion Vector times Matrix Product operation. QCD is the scientific theory that describes the interactions of various types of sub-atomic particles. Lattice QCD is the use of computer simulations to prove aspects of this theory. The research described in this paper aims to investigate whether FPGAs and logarithmic arithmetic are a viable compute-platform for high performance computing by implementing lattice QCD for this platform. We have achieved competitive performance of at least 936 MFlops per node, executing 14.2 floating point equivalent operations per cycle, which is far higher than the previous solutions proposed for lattice QCD simulations.