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In experiments requiring sentence comprehension, young children sometimes appear to accept coreference in sentences such as Thelma touched her. This has motivated the claim that 4- and 5-year-olds lack knowledge of the principles of binding and coreference. Another option, however, is that the requisite principles are present from the very start and children's poor performance is due to performance factors. We test this claim through a longitudinal analysis of the spontaneous speech of three children, analyzing their usage of the pronoun me and the reflexive myself. Even 2- and 3-year-olds virtually always use these forms in accord with the adult grammar—they will say John hit me and not John hit myself (obeying Principle A) and I hit myself and not I hit me (obeying Principle B). We argue that the best explanation for these results is that children understand the principles of binding and coreference at the earliest stages of language development.