It was something J.C.R. Licklider envisioned in the early 1960s when he was the first director of the Information Processing Techniques Office at ARPA.

https://en.wikipedia.org/wiki/Intergalactic_Computer_Network

M. Mitchell Waldrop delves into the history in his wonderful book about Licklider titled "The Dream Machine". Here's chapter one:

http://www.nytimes.com/2001/10/07/books/chapters/07-1st-wald...

Here's an example of a memo written by Licklider discussing the Intergalactic Computer Network:

http://worrydream.com/refs/Licklider-IntergalacticNetwork.pd...