dialogue (n.) Look up dialogue at Dictionary.com
early 13c., "literary work consisting of a conversation between two or more persons," from Old French dialoge, from Latin dialogus, from Greek dialogos "conversation, dialogue," related to dialogesthai "converse," from dia- "across" (see dia-) + legein "speak" (see lecture (n.)).

Sense broadened to "a conversation" c.1400. Mistaken belief that it can only mean "conversation between two persons" is from confusion of dia- and di- (1); the error goes back to at least 1532, when trialogue was coined needlessly for "a conversation between three persons." A word that has been used for "conversation between two persons" is the hybrid duologue (1864).