Space is a very important aspect in the simulation of biochemical models, recently, the need for simulation algorithms able to cope with space is becoming more and more compelling. Complex and large models of biochemical systems need to deal with the movement of single molecules and particles, taking into consideration localised fluctuations, transportation phenomena and diffusion. A common drawback of spatial models lies in their complexity: models could become very large, and their simulation could be time consuming, especially if we want to capture the systems behaviour in a reliable way using stochastic methods in conjunction with a high spatial resolution. In order to deliver the promise done by systems biology to be able to understand a system as whole, we need to move from sequential to parallel simulation algorithms. In this paper we analyse Smoldyn, a widely diffused algorithm for stochastic simulation of chemical reactions with spatial resolution and single molecule detail, and we propose an alternative, innovative implementation that exploits the parallelism of GPUs. The implementation offers good speedups (up to 130x) and real time, high quality graphics output at almost no performance penalties.