We propose an end-to-end neural model for zero-shot abstractive text summarization of paragraphs, and introduce a benchmark task, ROCSumm, based on ROCStories, a subset for which we collected human summaries. In this task, five-sentence stories (paragraphs) are summarized with one sentence, using human summaries only for evaluation. We show results for extractive and human baselines to demonstrate a large abstractive gap in performance. Our model, SummAE, consists of a denoising auto-encoder that embeds sentences and paragraphs in a common space, from which either can be decoded. Summaries for paragraphs are generated by decoding a sentence from the paragraph representations. We find that traditional sequence-to-sequence auto-encoders fail to produce good summaries and describe how specific architectural choices and pre-training techniques can significantly improve performance, outperforming extractive baselines. The data, training, evaluation code, and best model weights are open-sourced.