Gaussian Random Number Generators (GRNGs) are an important component in parallel Monte-Carlo simulations using FPGAs, where tens or hundreds of high-quality Gaussian samples must be generated per cycle using very few logic resources. This paper describes the Table-Hadamard generator, which is a GRNG designed to generate multiple streams of random numbers in parallel. It uses discrete table distributions to generate pseudo-Gaussian base samples, then a parallel Hadamard transform to efficiently apply the central limit theorem. When generating 64 output samples the Table-Hadamard requires just 130 slices per generated sample, which is a third of the resources needed by the next best technique, while still providing
higher statistical quality.