  The LIGO detection of the gravitational wave transient GW150914, from the
inspiral and merger of two black holes with masses $\gtrsim 30\,
\text{M}_\odot$, suggests a population of binary black holes with relatively
high mass. This observation implies that the stochastic gravitational-wave
background from binary black holes, created from the incoherent superposition
of all the merging binaries in the Universe, could be higher than previously
expected. Using the properties of GW150914, we estimate the energy density of
such a background from binary black holes. In the most sensitive part of the
Advanced LIGO/Virgo band for stochastic backgrounds (near 25 Hz), we predict
$\Omega_\text{GW}(f=25 Hz) = 1.1_{-0.9}^{+2.7} \times 10^{-9}$ with 90\%
confidence. This prediction is robustly demonstrated for a variety of formation
scenarios with different parameters. The differences between models are small
compared to the statistical uncertainty arising from the currently poorly
constrained local coalescence rate. We conclude that this background is
potentially measurable by the Advanced LIGO/Virgo detectors operating at their
projected final sensitivity.
