Signed languages such as American Sign Language (ASL) are natural languages that are formally similar to spoken languages, and thus present an opportunity to examine the effects of language structure and modality on the neural organization for language. Native learners of spoken languages show predominantly left-lateralized patterns of neural activation for language processing, whereas native learners of ASL show extensive right hemisphere (RH) and LH activation. We demonstrate that the RH angular gyrus is active during ASL processing only in native signers (hearing, ASL-English bilinguals) but not in those who acquired ASL after puberty (hearing, native English speakers). This is the first demonstration of a 'sensitive' or 'critical' period for language in an RH structure. This has implications for language acquisition and for understanding age-related changes in neuroplasticity more generally.