We present a new short-period brown dwarf candidate around the star TYC 1240-00945-1 . This candidate was discovered in the first year of the Multi-object APO Radial Velocity Exoplanets Large-area Survey ( MARVELS ) , which is part of the third phase of the Sloan Digital Sky Survey ( SDSS-III ) , and we designate the brown dwarf as MARVELS-1b . MARVELS uses the technique of dispersed fixed-delay interferometery to simultaneously obtain radial velocity measurements for 60 objects per field using a single , custom-built instrument that is fiber fed from the SDSS 2.5-m telescope . From our 20 radial velocity measurements spread over a \sim 370 d time baseline , we derive a Keplerian orbital fit with semi-amplitude K = 2.533 \pm 0.025 km s ^ { -1 } , period P = 5.8953 \pm 0.0004 d , and eccentricity consistent with circular . Independent follow-up radial velocity data confirm the orbit . Adopting a mass of 1.37 \pm 0.11 M _ { \odot } for the slightly evolved F9 host star , we infer that the companion has a minimum mass of 28.0 \pm 1.5 M _ { Jup } , a semimajor axis 0.071 \pm 0.002 AU assuming an edge-on orbit , and is probably tidally synchronized . We find no evidence for coherent instrinsic variability of the host star at the period of the companion at levels greater than a few millimagnitudes . The companion has an a priori transit probability of \sim 14 \% . Although we find no evidence for transits , we can not definitively rule them out for companion radii \lesssim 1 R _ { Jup } .