There is no accepted upper mass limit for stars. Such a basic quantity eludes both theory and observation, because of an imperfect understanding of the star-formation process and because of incompleteness in surveying the Galaxy. The Arches cluster is ideal for investigating such limits, being large enough to expect stars at least as massive as ~500 solar masses (~ 500Msolar based on a typical mass function), and young enough for its most massive members to still be visible. It is also old enough to be free of its natal molecular cloud, it is at a well-established distance, and it is close enough for us to discern its individual stars. Here I report an absence of stars with initial masses greater than 130Msolar in the Arches cluster, whereas the typical mass function predicts 18. I conclude that this indicates a firm limit of 150Msolar for stars; the probability that the observations are consistent with there being no upper limit is 10-8.