The call for a peremptory challenge procedure is based partially on dissatisfaction with existing mechanisms for judicial disqualification. Legislation and resolutions supporting peremptory challenges have come from several sources, although the judicial organizations have uniformly opposed it. The judiciary argues that such a change would greatly disrupt calendars, delay the beginning of criminal trials, inhibit judicial independence, and discourage judges from rendering unpopular opinions. The experience of the various States which permit peremptory challenges of trial judges provides support for both proponents and opponents of such challenges. Proponents can conclude that the use of the procedure is too limited to cause much of a problem, while opponents can conclude that the State statutes are unduly burdensome and invite misuse. Many administrative problems would result from permitting peremptory challenges in Federal courts, mainly because of the major differences between the Federal and State court systems. It is concluded that peremptory challenges would not resolve the common complaints about existing disqualification procedures. Instead of increasing public confidence in the judicial system as a whole, a peremptory challenge procedure would exacerbate any existing belief that judges are not to be trusted and that the system is an irrational one designed to allow legal maneuvering, manipulation, and sharp practice. Delays in justice and reduction in judicial independence might also occur. Peremptory challenges could stunt the growth of the law, which depends on imaginative and innovative insights of competent, independent judges. Footnotes and appendixes presenting legislation and American Bar Association resolutions are provided.