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 I recall a similar game, trying to reach and speak to an oracle. Specifically the Oracle of Syzygzy or something like that. Think it was a game that came with some Apple ][ magazine my parents got through work as teachers…