There is no accepted upper mass limit for stars. Such a basic quantity escapes both theory, because of incomplete understanding of star formation, and observation, because of incompleteness in surveying the Galaxy. The Arches cluster is ideal for such a test, being massive enough to expect stars at least as massive as 400 solar masses, and young enough for its most massive members to still be visible. It is old enough to be free of its natal molecular cloud, and close enough, and at a well-established distance, for us to discern its individual stars. Here I report an absence of stars with initial masses greater than 130 M in the Arches cluster, where the typical mass function predicts 18. I conclude that this indicates a firm limit of 150 M for stars as the probability that the observations are consistent with no limit is 10-8.