We present a robust neural abstractive summarization system for cross-lingual summarization. We construct summarization corpora for documents automatically translated from three low-resource languages, Somali, Swahili, and Tagalog, using machine translation and the New York Times summarization corpus. We train three language-specific abstractive summarizers and evaluate on documents originally written in the source languages, as well as on a fourth, unseen language: Arabic. Our systems achieve significantly higher fluency than a standard copy-attention summarizer on automatically translated input documents, as well as comparable content selection.