This paper illustrates the design and implementation of a prototype ASP solver that is capable of exploiting the parallelism offered by general purpose graphical processing units (GPGPUs). The solver is based on a basic conflictdriven search algorithm. The core of the solving process develops on the CPU, while most of the activities, such as literal selection, unit propagation, and conflictanalysis, are delegated to the GPU. Moreover, a deep non-deterministic search, involving a very large number of threads, is also delegated to the GPU. The initial results confirm the feasibility of the approach and the potential offered by GPUs in the context of ASP computations.