We model the accretion of gas onto a population of massive primordial black holes in the Milky Way and compare the predicted radio and x-ray emission with observational data. We show that, under conservative assumptions on the accretion process, the possibility that O(10)M_{⊙} primordial black holes can account for all of the dark matter in the Milky Way is excluded at 5σ by a comparison with a Very Large Array radio catalog at 1.4 GHz and at ≃40σ by a comparison with a Chandra x-ray catalog (0.5-8 keV). We argue that this method can be used to identify such a population of primordial black holes with more sensitive future radio and x-ray surveys.