Grounding referring expressions to objects in an environment has traditionally been considered a one-off, ahistorical task. However, in realistic applications of grounding, multiple users will repeatedly refer to the same set of objects. As a result, past referring expressions for objects can provide strong signals for grounding subsequent referring expressions. We therefore reframe the grounding problem from the perspective of coreference detection and propose a neural network that detects when two expressions are referring to the same object. The network combines information from vision and past referring expressions to resolve which object is being referred to. Our experiments show that detecting referring expression coreference is an effective way to ground objects described by subtle visual properties, which standard visual grounding models have difficulty capturing. We also show the ability to detect object coreference allows the grounding model to perform well even when it encounters object categories not seen in the training data.