Galactic stellar‐population‐synthesis models, chemical‐enrichment models, and possibly gravitational microlensing indicate that about Ntot=108–109 stellar‐mass black holes reside in our Galaxy. We study X‐ray emission from accretion from the interstellar medium on to isolated black holes. Although black holes may be fewer in number than neutron stars, NNS∼109, their higher masses, 〈M〉∼9 M⊙, and smaller space velocities, σv∼40 km s‐1, result in Bondi–Hoyle accretion rates ∼4×103 times higher than for neutron stars. Given a total number of black holes Ntot=N9109 within the Milky Way, we estimate that ∼103N9 should accrete at M˙>1015 g s‐1, comparable to accretion rates inferred for black hole X‐ray binaries. If black holes accrete at the Bondi–Hoyle rate with efficiencies only ∼10−4(NNS/Ntot)0.8 of the neutron‐star accretion efficiency, a comparable number of each may be detectable. We make predictions for the number of isolated accreting black holes in our Galaxy that can be detected with X‐ray surveys as a function of efficiency, concluding that all‐sky surveys at a depth of F=F‐1510‐15 erg cm‐2 s‐1 dex‐1 can find N(>F)∼104N9(F‐15/ε‐5)‐1.2 isolated accreting black holes for a velocity dispersion of 40 km s−1 and an X‐ray accretion efficiency of ε=ε‐510‐5. Deeper surveys of the Galactic plane with Chandra or XMM‐Newton may find tens of these objects per year, depending on the efficiency. We argue that a mass estimate can be derived for microlensing black hole candidates with an X‐ray detection.