The Kepler spacecraft is monitoring more than 150,000 stars for evidence of planets transiting those stars. We report the detection of two Saturn-size planets that transit the same Sun-like star, based on 7 months of Kepler observations. Their 19.2- and 38.9-day periods are presently increasing and decreasing at respective average rates of 4 and 39 minutes per orbit; in addition, the transit times of the inner body display an alternating variation of smaller amplitude. These signatures are characteristic of gravitational interaction of two planets near a 2:1 orbital resonance. Six radial-velocity observations show that these two planets are the most massive objects orbiting close to the star and substantially improve the estimates of their masses. After removing the signal of the two confirmed giant planets, we identified an additional transiting super-Earth–size planet candidate with a period of 1.6 days.