TYC 4110-01037-1 has a low-mass stellar companion, whose small mass ratio and short orbital period are atypical among binary systems with solar-like (T eff <~ 6000 K) primary stars. Our analysis of TYC 4110-01037-1 reveals it to be a moderately aged (lsim5 Gyr) solar-like star having a mass of 1.07 ± 0.08 M &sun; and radius of 0.99 ± 0.18 R &sun;. We analyze 32 radial velocity (RV) measurements from the SDSS-III MARVELS survey as well as 6 supporting RV measurements from the SARG spectrograph on the 3.6 m Telescopio Nazionale Galileo telescope obtained over a period of ~2 years. The best Keplerian orbital fit parameters were found to have a period of 78.994 ± 0.012 days, an eccentricity of 0.1095 ± 0.0023, and a semi-amplitude of 4199 ± 11 m s-1. We determine the minimum companion mass (if sin i = 1) to be 97.7 ± 5.8 M Jup. The system's companion to host star mass ratio, >=0.087 ± 0.003, places it at the lowest end of observed values for short period stellar companions to solar-like (T eff <~ 6000 K) stars. One possible way to create such a system would be if a triple-component stellar multiple broke up into a short period, low q binary during the cluster dispersal phase of its lifetime. A candidate tertiary body has been identified in the system via single-epoch, high contrast imagery. If this object is confirmed to be comoving, we estimate it would be a dM4 star. We present these results in the context of our larger-scale effort to constrain the statistics of low-mass stellar and brown dwarf companions to FGK-type stars via the MARVELS survey.