Parenago 1802, a member of the ~1 Myr Orion Nebula Cluster, is a double-lined, detached eclipsing binary in a 4.674 d orbit, with equal-mass components (M_2/M_1 = 0.985 pm 0.029). Here we present extensive VIcJHKs light curves spanning ~15 yr, as well as a Keck/HIRES optical spectrum. The light curves evince a third light source that is variable with a period of 0.73 d, and is also manifested in the high-resolution spectrum, strongly indicating the presence of a third star in the system, probably a rapidly rotating classical T Tauri star. We incorporate this third light into our radial velocity and light curve modeling of the eclipsing pair, measuring accurate masses (M_1 = 0.391 pm 0.032, M_2 = 0.385 pm 0.032 Modot), radii (R_1 = 1.73 pm 0.02, R_2 = 1.62 pm 0.02 Rodot), and temperature ratio (T_1/T_2 = 1.0924 pm 0.0017). Thus the radii of the eclipsing stars differ by 6.9 pm 0.8%, the temperatures differ by 9.2 pm 0.2%, and consequently the luminosities differ by 62 pm 3%, despite having masses equal to within 3%. This could be indicative of an age difference of ~3x10^5 yr between the two eclipsing stars, perhaps a vestige of the binary formation history. We find that the eclipsing pair is in an orbit that has not yet fully circularized, e = 0.0166 pm 0.003. In addition, we measure the rotation rate of the eclipsing stars to be 4.629 pm 0.006 d; they rotate slightly faster than their 4.674 d orbit. The non-zero eccentricity and super-synchronous rotation suggest that the eclipsing pair should be tidally interacting, so we calculate the tidal history of the system according to different tidal evolution theories. We find that tidal heating effects can explain the observed luminosity difference of the eclipsing pair, providing an alternative to the previously suggested age difference.
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