Multilingual question answering tasks typically assume that answers exist in the same language as the question. Yet in practice, many languages face both information scarcity---where languages have few reference articles---and information asymmetry--
-where questions reference concepts from other cultures. This work extends open-retrieval question answering to a cross-lingual setting enabling questions from one language to be answered via answer content from another language. We construct a large-scale dataset built on 40K information-seeking questions across 7 diverse non-English languages that TyDi QA could not find same-language answers for. Based on this dataset, we introduce a task framework, called Cross-lingual Open-Retrieval Question Answering (XOR QA), that consists of three new tasks involving cross-lingual document retrieval from multilingual and English resources. We establish baselines with state-of-the-art machine translation systems and cross-lingual pretrained models. Experimental results suggest that XOR QA is a challenging task that will facilitate the development of novel techniques for multilingual question answering. Our data and code are available at https://nlp.cs.washington.edu/xorqa/.
