We address the problem of predicting psychiatric hospitalizations using linguistic features drawn from social media posts. We formulate this novel task and develop an approach to automatically extract time spans of self-reported psychiatric hospitalizations. Using this dataset, we build predictive models of psychiatric hospitalization, comparing feature sets, user vs. post classification, and comparing model performance using a varying time window of posts. Our best model achieves an F1 of .718 using 7 days of posts. Our results suggest that this is a useful framework for collecting hospitalization data, and that social media data can be leveraged to predict acute psychiatric crises before they occur, potentially saving lives and improving outcomes for individuals with mental illness.