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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-circle dot, and thus it is a high-confidence BD companion. It has a moderately long orbital period of 47.8929(-0.0062) (+0.0063) days with a low eccentricty of 0.1442(-0.0073)(+0.0078), and a semi-amplitude of 1644(-13)(+12) 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-circle dot = 1.11 +/- 0.11 M-circle dot and R-* = 1.06 +/- 0.23 R-circle dot with an age consistent with less than similar to 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 arcsec 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.