  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_Sun in the Arches cluster, where the typical mass function predicts
18. I conclude that this indicates a firm limit of 150 M_Sun for stars as the
probability that the observations are consistent with no limit is 10^-8.
