KOI-55 is a hot B-type star (about 0.50 solar masses, 27,730 K, 0.20 solar radii), 1,231 light-years from Earth. KOI-55 b is a 0.4-Earth-mass planet, with an orbital period of 5.8 hours, at 0.006 AU from its star, discovered in 2011 via orbital brightness modulation. KOI-55 c is a 0.7-Earth-mass planet, with an orbital period of 8.2 hours, at 0.008 AU from its star, discovered in 2011 via orbital brightness modulation. KOI-55 adds another data point to the growing catalogue of planetary systems whose masses, orbits, and host-star properties constrain models of planet formation.