We report the detection of GJ 832c, a super-Earth orbiting near the inner edge of the habitable zone of GJ 832, an M dwarf previously known to host a Jupiter analog in a nearly circular 9.4 yr orbit. The combination of precise radial-velocity measurements from three telescopes reveals the presence of a planet with a period of 35.68 +/- 0.03 days and minimum mass (m sin i) of 5.4 +/- 1.0 Earth masses. GJ 832c moves on a low-eccentricity orbit (e = 0.18 +/- 0.13) toward the inner edge of the habitable zone. However, given the large mass of the planet, it seems likely that it would possess a massive atmosphere, which may well render the planet inhospitable. Indeed, it is perhaps more likely that GJ 832c is a "super-Venus," featuring significant greenhouse forcing. With an outer giant planet and an interior, potentially rocky planet, the GJ 832 planetary system can be thought of as a miniature version of our own solar system.