We propose a model for tagging unstructured texts with an arbitrary number of terms drawn from a tree-structured vocabulary (i.e., an ontology). We treat this as a special case of sequence-to-sequence learning in which the decoder begins at the root node of an ontological tree and recursively elects to expand child nodes as a function of the input text, the current node, and the latent decoder state. We demonstrate that this method yields state-of-the-art results on the important task of assigning MeSH terms to biomedical abstracts.