There will be significant improvement of computer chess software performance and computers will beat the best human players by 1998, and most likely in that year.
In fact, the prediction became true even a year before - in May 1997 when chess World Champion Garry Kasparov was defeated by IBM's Deep Blue computer in a well-publicized chess tournament.
Kurzweil, Ray. 1990. The age of intelligent machines. Cambridge, Mass: MIT Press.