We introduce an attentional neural machine translation model for the task of machine translation that accomplishes the longstanding goal of natural language processing to take advantage of the hierarchical structure of language without a priori annotation. The model comprises a recurrent neural network grammar (RNNG) encoder with a novel attentional RNNG decoder and applies policy gradient reinforcement learning to induce unsupervised tree structures on both the source sequence and target sequence. When trained on character-level datasets with no explicit segmentation or parse annotation, the model learns a plausible segmentation and shallow parse, obtaining performance close to an attentional baseline.