We report the discovery and characterization of a new M-dwarf binary, with component masses and radii of M_1_=0.244_-0.003_^+0.003^M_{sun}_, R_1_=0.261_-0.009_^+0.006^R_{sun}_, M_2_=0.179_-0.001_^+0.002^M_{sun}_, R_2_=0.218_-0.011_^+0.007^R_{sun}_, and orbital period of ~4.1 d. The M-dwarf binary HATS551-027 (LP 837-20) was identified as an eclipsing binary by the HATSouth survey, and characterized by a series of high-precision photometric observations of the eclipse events, and spectroscopic determinations of the atmospheric parameters and radial velocity orbits. HATS551-027 is one of few systems with both stellar components lying in the fully convective regime of very low mass stars, and can serve as a test for stellar interior models. The radius of HATS551-027A is consistent with models to 1{sigma}, whilst HATS551-027B is inflated by 9 percent at 2{sigma} significance. We measure the effective temperatures for the two stellar components to be T_eff,1_=3190+/-100K and T_eff,2_=2990+/-110K; both are slightly cooler than theoretical models predict, but consistent with other M-dwarfs of similar masses that have previously been studied. We also measure significant H{alpha} emission from both components of the binary system, and discuss this in the context of the correlation between stellar activity and the discrepancies between the observed and model temperatures.