This paper examines the fluid behavior in micro and nano sized channels by using a coupled Molecular Dynamics and Lattice Boltzmann solution method, implemented in a novel fashion on a Graphics Processor. Molecular Dynamics is well known for its ability to resolve phenomena in the near wall regions, where continuum assumptions are no longer valid, at the expense of computational power. Lattice Boltzmann is a mesoscale continuum-description solver that is very efficient and reduces to the Navier-Stokes equations, thereby being a logical choice to solve regions further from the wall. This method is parallelized to be run on the Graphics Processor, using NVIDIA's CUDA programming language. Individually, Lattice Boltzmann methods are approximately 70x faster on the GPU than a modern CPU, Molecular Dynamics is about 5x faster. Higher resolutions are able to be simulated than previously performed due to the efficiency of this implementation. We analyze the results of straight channel Poiseuille flow using the hybrid solver and note the continuum breakdown is successfully predicted by the hybrid code in the form of density oscillations near the wall along with velocity slip conditions. Streamlines, contours and velocity profiles are utilized to illustrate these points. Future work includes expanding this solver's capability to handle complex boundaries.