IoT big data requires new machine learning methods able to scale to large size of data arriving at high speed. Decision trees are popular machine learning models since they are very effective, yet easy to interpret and visualize. In the literature, we can find distributed algorithms for learning decision trees, and also streaming algorithms, but not algorithms that combine both features. In this paper we present the Vertical Hoeffding Tree (VHT), the first distributed streaming algorithm for learning decision trees. It features a novel way of distributing decision trees via vertical parallelism. The algorithm is implemented on top of Apache SAMOA, a platform for mining big data streams, and thus able to run on real-world clusters. Our experiments to study the accuracy and throughput of VHT prove its ability to scale while attaining superior performance compared to sequential decision trees.