A variety of applications employ ensemble learning models, using a collection of decision trees, to quickly and accurately classify an input based on its vector of features. In this paper, we discuss the implementation of such a method, namely Random Forests, as the first machine learning algorithm to be executed on the Automata Processor (AP). The AP is an upcoming reconfigurable co-processor accelerator which supports the execution of numerous automata in parallel against a single input data-flow. Owing to this execution model, our approach is fundamentally different, translating Random Forest models from existing memory-bound tree-traversal algorithms to pipelined designs that use multiple automata to check all of the required thresholds independently and in parallel. We also describe techniques to handle floating-point feature values which are not supported in the native hardware, pipelining of the execution stages, and compression of automata for the fastest execution times. The net result is a solution which when evaluated using two applications, namely handwritten digit recognition and sentiment analysis, produce up to 63 and 93 times speed-up respectively over single-core state-of-the-art CPU-based solutions. We foresee these algorithmic techniques to be useful not only in the acceleration of other applications employing Random Forests, but also in the implementation of other machine learning methods on this novel architecture.