The first computer I used with speech synthesis was an Amiga 1000 in 1985. However, it wasn't anything you would confuse with a human voice - early speech synthesis sounded very artificial and required phonetic input for (relatively) good results. I think there were chips specifically for speech synthesis pretty early, too, that were used in lower-cost devices than microcomputers.
eg. Votrax SC-01, and friends. See Doug McIlroy's paper "Synthetic English speech by rule", Bell Telephone Laboratories CSTR #14 (1974) (available from http://www.cs.dartmouth.edu/~doug/pubs.html)
