Glossolalia

glossolalia \ˌglä-sə-ˈlā-lē-ə\ noun: ecstatic usually unintelligible utterance usually accompanying religious excitation

Etymology: New Latin, from Greek glōss-, glōsso-, from glōssa tongue, language + lalia chatter, from lalein to chat

This is the same thing as “speaking in tongues,” which is itself a pretty funny phrase if you imagine tongues to be not languages, but, well, honest-to-goodness tongues.