We have discovered four intergalactic H II regions in Stephan's quintet, which is more than a 25 kpc projected distance from the center of the nearest group galaxy, with no apparent optical connection to it. They have MB ranging from -11.9 to -12.5 mag, colors B-R=0.7-1.1 mag, radial velocities from 6565 to 6651 km s-1, and they are superposed onto the H I tail east of NGC 7319, with a mean radial velocity of 6610 km s-1. In addition, they have metallicities of the order of 12+log(O/H)=8.58+/-0.25, which suggests that they were formed from preenriched material. We derive a mean age of 4.6+/-0.6 Myr and a mean stellar mass of (2.9+/-1.4)×104 Msolar for the four objects. The masses, ages, colors, velocities, metallicities, and location of the objects suggest that they are H II regions that were formed far away from the galaxies through compression of the intergalactic H I gas by galaxy collisions.Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (US), the Particle Physics and Astronomy Research Council (UK), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil), and CONICET (Argentina).