  We prove that the moduli space of gauge equivalence classes of symplectic
vortices with uniformly bounded energy in a compact Hamiltonian manifold admits
a Gromov compactification by polystable vortices. This extends results of
Mundet i Riera and Tian for circle actions to the case of arbitrary compact Lie
groups. Our argument relies on an a priori estimate for vortices that allows us
to apply techniques used by McDuff and Salamon in their proof of Gromov
compactness for pseudoholomorphic curves. As an intermediate result we prove a
removable singularity theorem for vortices.
