While ELT has long recognized the need to address student anxiety in language learning situations, it has all too often assumed that such anxiety is primarily competence-based. Consequently, there has been insufficient recognition of the fact that identity-based anxiety, too, can have significant effects on language learning in the classroom. In this paper, we discuss some examples of identity-based anxiety, and argue that it requires a different approach to language teaching. We propose one such possible approach, which we call "double-crossing".