Decades of extensive research efforts by biochemists, organic chemists, and protein engineers have led to an understanding of the basic mechanisms of essentially all known types of enzymes, but in a formidable number of cases an essential aspect has been overlooked. The occurrence of short-lived chiral intermediates formed by symmetry-breaking of prochiral precursors in enzyme catalyzed reactions has been systematically neglected. We designate these elusive species as fleeting chiral intermediates and analyze such crucial questions as "Do such intermediates occur in homochiral form?" If so, what is the absolute configuration, and why did Nature choose that particular stereoisomeric form, even when the isolable final product may be achiral? Does the absolute configuration of a chiral product depend in any way on the absolute configuration of the fleeting chiral precursor? How does this affect the catalytic proficiency of the enzyme? If these issues continue to be unexplored, then an understanding of the mechanisms of many enzyme types remains incomplete. We have systematized the occurrence of these chiral intermediates according to their structures and enzyme types. This is followed by critical analyses of selected case studies and by final conclusions and perspectives. We hope that the fascinating concept of fleeting chiral intermediates will attract the attention of scientists, thereby opening an exciting new research field.