My first recollection of having a "conversation" on a computer was ~1984. It was a text-based game on the Apple II that I can't remember the name of, but at some point in the game you could end up in a church or temple, and you could ask it anything. Of course, the game was limited in the number of different answers it could give at random, but the answers were all general and sagacious enough that they could be interpreted as some kind of meaningful response (at least to a 12 y/o). Wish I could recall the name of the game. Anyone?
@briankrebs If it was 1985 and you were answering (rather than asking) questions, it might be the ending of Ultima IV, where you use the stones to go down each level -- and the final stone takes you to a black screen and you have to answer a series of questions about the virtues as it slowly draws the symbol of the Codex of Ultimate Wisdom with each correct answer. Felt profound when I played it around the same time (at about the same age).