Soon after the discovery of the Kerr metric, Penrose realized that superradiance can be exploited to extract energy from black holes. The original idea (involving the breakup of a single particle) yields only modest energy gains. A variant of the Penrose process consists of particle collisions in the ergoregion. The collisional Penrose process has been explored recently in the context of dark matter searches, with the conclusion that the ratio eta between the energy of postcollision particles detected at infinity and the energy of the colliding particles should be modest (eta less than or similar to 1.5). Schnittman [Phys. Rev. Lett. 113, 261102 (2014)] has shown that these studies underestimated the maximum efficiency by about 1 order of magnitude (i.e., eta less than or similar to 15). In this work we show that particle collisions in the vicinity of rapidly rotating black holes can produce high-energy ejecta and result in high efficiencies under much more generic conditions. The astrophysical likelihood of these events deserves further scrutiny, but our study hints at the tantalizing possibility that the collisional Penrose process may power gamma rays and ultrahigh-energy cosmic rays.