Coreference resolution is an important task for natural language understanding, and the resolution of ambiguous pronouns a longstanding challenge. Nonetheless, existing corpora do not capture ambiguous pronouns in sufficient volume or diversity to accurately indicate the practical utility of models. Furthermore, we find gender bias in existing corpora and systems favoring masculine entities. To address this, we present and release GAP, a gender-balanced labeled corpus of 8,908 ambiguous pronoun-name pairs sampled to provide diverse coverage of challenges posed by real-world text. We explore a range of baselines which demonstrate the complexity of the challenge, the best achieving just 66.9% F1. We show that syntactic structure and continuous neural models provide promising, complementary cues for approaching the challenge.