Random Forest is a classical ensemble method used to improve the performance of single tree classifiers. It is able to obtain superior performance by increasing the diversity of the single classifiers. However, in the more challenging context of evolving data streams, the classifier has also to be adaptive and work under very strict constraints of space and time. Furthermore, the computational load of using a large number of classifiers can make its application extremely expensive. In this work, we present a method for building Random Forests that use Very Fast Decision Trees for data streams on GPUs. We show how this method can benefit from the massive parallel architecture of GPUs, which are becoming an efficient hardware alternative to large clusters of computers. Moreover, our algorithm minimizes the communication between CPU and GPU by building the trees directly inside the GPU. We run an empirical evaluation and compare our method to two well know machine learning frameworks, VFML and MOA. Random Forests on the GPU are at least 300x faster while maintaining a similar accuracy.