Graphical processing units (GPUs) are rapidly outpacing conventional CPUs in computational performance. The authors provide a brief overview of electronic structure theory and detail their experiences implementing quantum chemistry methods on the GPU, demonstrating speedups of up to 93x for direct self-consistent field calculations on a variety of molecules. They analyze the performance of the algorithms in terms of floating-point operations and memory bandwidth. They also assess the adequacy of the single-precision accuracy for quantum chemistry applications.