Primordial black holes (PBHs) have long been suggested as a candidate for making up some or all of the dark matter in the Universe. Most of the theoretically possible mass range for PBH dark matter has been ruled out with various null observations of expected signatures of their interaction with standard astrophysical objects. However, current constraints are significantly less robust in the 20 M☉≲MPBH≲100 M☉ mass window, which has received much attention recently, following the detection of merging black holes with estimated masses of ̃30 M☉ by LIGO and the suggestion that these could be black holes formed in the early Universe. We consider the potential of advanced LIGO (aLIGO) operating at design sensitivity to probe this mass range by looking for peaks in the mass spectrum of detected events. To quantify the background, which is due to black holes that are formed from dying stars, we model the shape of the stellar-black-hole mass function and calibrate its amplitude to match the O 1 results. Adopting very conservative assumptions about the PBH and stellar-black-hole merger rates, we show that ̃5 yr of aLIGO data can be used to detect a contribution of >20 M☉ PBHs to dark matter down to fPBH<0.5 at >99.9 % confidence level. Combined with other probes that already suggest tension with fPBH=1 , the obtainable independent limits from aLIGO will thus enable a firm test of the scenario that PBHs make up all of dark matter.