Apsidal Motion of the Massive, Benchmark Eclipsing Binary V578 Mon

V578 Mon is a system of two early B-type stars in the Rosette Nebula star-forming region (NGC 2244) and is one of only nine eclipsing binaries with component masses greater than 10 M whose physical parameters have been determined with an accuracy of better than 3%. It is therefore a benchmark system for evolutionary and stellar structure models of newly formed massive stars. Combining our multi-band light curves spanning 40 yr with previous light curve data from the literature, we fit a model light curve that for the first time includes the effects of apsidal motion of the system. We measure an apsidal period of 33.48+0.10 -- 0.06 yr. As a consequence of incorporating the apsidal motion into the modeling of the system's orbital parameters, we determine an updated eccentricity of e = 0.07755+0.00022 -- 0.00027, which differs significantly from the value previously reported in the literature. Evidently, the inclusion of apsidal motion in the light curve modeling significantly affects the eccentricity determination. Incorporating these key parameters into a comprehensive model of the system's physical parameters--including internal structure constraints--will bring V578 Mon to the next level of benchmark precision and utility.