In this paper, we present an accurate and extensible approach for the coreference resolution task. We formulate the problem as a span prediction task, like in machine reading comprehension (MRC): A query is generated for each candidate mention using its surrounding context, and a span prediction module is employed to extract the text spans of the coreferences within the document using the generated query. This formulation comes with the following key advantages: (1) The span prediction strategy provides the flexibility of retrieving mentions left out at the mention proposal stage; (2) In the MRC framework, encoding the mention and its context explicitly in a query makes it possible to have a deep and thorough examination of cues embedded in the context of coreferent mentions; and (3) A plethora of existing MRC datasets can be used for data augmentation to improve the model's generalization capability. Experiments demonstrate significant performance boost over previous models, with 87.5 (+2.5) F1 score on the GAP benchmark and 83.1 (+3.5) F1 score on the CoNLL-2012 benchmark.