The LIGO detection of the gravitational wave transient GW150914, from the inspiral and merger of twoblack holes with masses≳30M⊙, suggests a population of binary black holes with relatively high mass. Thisobservation implies that the stochastic gravitational-wave background from binary black holes, created fromthe incoherent superposition of all the merging binaries in the Universe, could be higher than previouslyexpected. Using the properties of GW150914, we estimate the energy density of such a background frombinary black holes. In the most sensitive part of the Advanced LIGO and AdvancedVirgo band for stochasticbackgrounds (near 25 Hz), we predict ΩGW(f = 25 Hz) = 1.1+2.7−0.9 × 10^(−9) with 90% confidence. Thisprediction is robustly demonstrated for a variety of formation scenarios with different parameters. Thedifferences betweenmodels are small compared to the statistical uncertainty arising from the currently poorlyconstrained local coalescence rate. We conclude that this background is potentially measurable by theAdvanced LIGO and Advanced Virgo detectors operating at their projected final sensitivity.