To speak in a language unknown to the speaker, especially when in a state of religious ecstasy; glossolalia.

speaking in tongues

Third-person singular simple present indicative form of speak in tongues

The act of speaking a language one does not know, or speaking elaborate but apparently meaningless speech, while in a trance-like state (or, supposedly, under the influence of a deity or spirits); glossolalia.

present participle of speak in tongues.