  The merger rate of black hole binaries inferred from the detections in the
first Advanced LIGO science run, implies that a stochastic background produced
by a cosmological population of mergers will likely mask the primordial
gravitational-wave background. Here we demonstrate that the next generation of
ground-based detectors, such as the Einstein Telescope and Cosmic Explorer,
will be able to observe binary black hole mergers throughout the universe with
sufficient efficiency that the confusion background can potentially be
subtracted to observe the primordial background at the level of
$\Omega_{\mathrm{GW}} \simeq 10^{-13}$ after five years of observation.
