Is there a limit to what computers can do? In many areas, the facts of today put the sceptics of yesterday in the wrong. Who would have thought twenty years ago that a chess computer could ever beat the human world champion? With respect to computer programs for solving legal problems, the question is not whether they are possible, for they exist. In law, at least two important questions remain. First, whether such programs can eventually perform as good as, or better than humans. Second, whether the use of computers will alter the law and legal adjudication. These two questions are discussed in this article against the background of a comparison of chess and law. The answers give rise to certain premonitions. If the computer is used as an aid in legal decision making, it should be used in awareness of its limitations and idiosyncrasies.