  We show that complex, massive spin-1 fields minimally coupled to Einstein's
gravity with a negative cosmological constant, admit asymptotically anti-de
Sitter self-gravitating solutions. Focusing on 4-dimensional spacetimes, we
start by obtaining analytical solutions in the test-field limit, where the
Proca field equations can be solved in a fixed anti-de Sitter background, and
then find fully non-linear solutions numerically. These solutions are a natural
extension of the recently found asymptotically flat Proca stars and share
similar properties with scalar boson stars. In particular, we show that they
are stable against spherically symmetric linear perturbations for a range of
fundamental frequencies limited by their point of maximum mass. We finish with
an overview of the behavior of Proca stars in $5$ dimensions.
