We describe the discovery of a likely brown dwarf (BD) companion with a minimum mass of 31.7 ± 2.0 M Jup to GSC 03546-01452 from the MARVELS radial velocity survey, which we designate as MARVELS-6b. For reasonable priors, our analysis gives a probability of 72% that MARVELS-6b has a mass below the hydrogen-burning limit of 0.072 M ☉, and thus it is a high-confidence BD companion. It has a moderately long orbital period of 47.8929^{+0.0063}_{-0.0062} days with a low eccentricity of 0.1442^{+0.0078}_{-0.0073}, and a semi-amplitude of 1644^{+12}_{-13} m s–1. Moderate resolution spectroscopy of the host star has determined the following parameters: T eff = 5598 ± 63, log g = 4.44 ± 0.17, and [Fe/H] = +0.40 ± 0.09. Based upon these measurements, GSC 03546-01452 has a probable mass and radius of M * = 1.11 ± 0.11 M ☉ and R * = 1.06 ± 0.23 R ☉ with an age consistent with less than ~6 Gyr at a distance of 219 ± 21 pc from the Sun. Although MARVELS-6b is not observed to transit, we cannot definitively rule out a transiting configuration based on our observations. There is a visual companion detected with Lucky Imaging at 7.''7 from the host star, but our analysis shows that it is not bound to this system. The minimum mass of MARVELS-6b exists at the minimum of the mass functions for both stars and planets, making this a rare object even compared to other BDs. It also exists in an underdense region in both period/eccentricity and metallicity/eccentricity space.