We introduce deep inside-outside recursive autoencoders (DIORA), a fully-unsupervised method for discovering syntax that simultaneously learns representations for constituents within the induced tree. Our approach predicts each word in an input sentence conditioned on the rest of the sentence and uses inside-outside dynamic programming to consider all possible binary trees over the sentence. At test time the CKY algorithm extracts the highest scoring parse. DIORA achieves a new state-of-the-art F1 in unsupervised binary constituency parsing (unlabeled) in two benchmark datasets, WSJ and MultiNLI.