A high-resolution Direct Numerical Simulation (DNS) of incompressible turbulent flow in a square duct has been conducted to demonstrate the capability of a Navier-Stokes solver implemented on a Graphics Processing Unit (GPU). The simulation used a frictional Reynolds number of 360 and a mesh of 26.2 million cells. The code was written for a GPU using CUDA (Compute Unified Device Architecture), a programming paradigm developed by NVIDIA. The GPU has permitted fast, high-resolution calculations on a rather inexpensive computer, opening up new opportunities to efficiently conduct Direct and Large Eddy Simulations of turbulent flows. Implementation details and code performance will be discussed.