The social Web is a widely used platform for online discussion. Across social media, users can start discussions by posting a topical image, url, or message. Upon seeing this initial post, other users may add their own comments to the post, or to another user's comment. The resulting online discourse produces a comment thread, which constitutes an enormous portion of modern online communication. Comment threads are often viewed as trees: nodes represent the post and its comments, while directed edges represent reply-to relationships. The goal of the present work is to predict the size and shape of these comment threads. Existing models do this by observing the first several comments and then fitting a predictive model. However, most comment threads are relatively small, and waiting for data to materialize runs counter to the goal of the prediction task. We therefore introduce the Comment Thread Prediction Model (CTPM) that accurately predicts the size and shape of a comment thread using only the text of the initial post, allowing for the prediction of new posts without observable comments. We find that the CTPM significantly outperforms existing models and competitive baselines on thousands of Reddit discussions from nine varied subreddits, particularly for new posts.