Well, Modderfokker, if you're referring to network when you say system, that was ARPANET, the Internet's Great-Grandfather, way back in October of 1969.

And if you mean computer system, it was an SDS 940 at Stanford had the first telnet functionality, and the first remote telnet session was over ARPANET between the SDS 940 and a Sigma 7 at UCLA.

69 was a good year....Hell, 69 is just plain good!

And FYI, I think the first microcomputer to use telnet was the Altair 8800, back in '75.