We determine the age distribution of star clusters in the Antennae galaxies (NGC 4038/9) for two mass-limited samples (M > 3 x 10 super(4) M sub( )and M > 2 x 10 super(5) M sub( )). This is based on integrated broadband UBVI and narrowband Ha photometry from deep images taken with the Hubble Space Telescope. We find that the age distribution of the clusters declines steeply, approximately as dN/dt 8 t super(-1). The median age of the clusters is 610 super(7) yr, which we interpret as evidence for rapid disruption ("infant mortality"). It is very likely that most of the young clusters are not gravitationally bound and were disrupted near the times they formed by the energy and momentum input from young stars to the interstellar matter of the protoclusters. At least 20% and possibly all stars form in clusters and/or associations, including those that are unbound and short-lived.