  We show that binaries of stellar-mass black holes formed inside a young
protoglobular cluster, can grow rapidly inside the cluster's core by accretion
of the intracluster gas, before the gas may be depleted from the core. A black
hole with mass of the order of eight solar masses can grow to values of the
order of thirty five solar masses in accordance with recent gravitational waves
signals observed by LIGO. Due to the black hole mass increase, a binary may
also harden. The growth of binary black holes in a dense protoglobular cluster
through mass accretion indicates a potentially important formation and
hardening channel.
