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During slow-roll inflation, nonperturbative transitions can produce bubbles of metastable vacuum. These bubbles expand exponentially during inflation to superhorizon size, and later collapse into black holes when the expansion of the Universe is decelerating. Estimating the rate for these transitions during a time-dependent slow-roll phase requires the development of new techniques. Our results show that in a broad class of models, the inflationary fine-tuning that gives rise to small density fluctuations causes these bubbles to appear only during a time interval that is short compared to the inflationary Hubble time. As a result, despite the fact that the final mass of the black hole is exponentially sensitive to the moment bubbles form during inflation, the resulting primordial black hole mass spectrum can be nearly monochromatic. If the transition occurs near the middle of inflation, the mass can fall in the “asteroid” range ${10}^{17}–{10}^{22}\mathrm{g}$in which all known observations are compatible with black holes comprising 100% of dark matter.