Parenago 1802, a member of the ~1 Myr Orion Nebula Cluster, is a double-lined, detached eclipsing binary in a 4.674 day orbit, with equal-mass components (M_2_/M_1_=0.985+/-0.029). Here we present extensive VI_C_JHK_S_light curves (LCs) spanning ~15 yr, as well as a Keck/High Resolution Echelle Spectrometer (HIRES) optical spectrum. The LCs evince a third light source that is variable with a period of 0.73 days, 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 LC modeling of the eclipsing pair, measuring accurate masses (M_1_=0.391+/-0.032 and M_2_=0.385+/-0.032M_{sun}_), radii (R_1_=1.73+/-0.02 and R_2_=1.62+/-0.02R_{sun}_), and temperature ratio (T_eff,1_/T_eff,2_=1.0924+/-0.0017). Thus, the radii of the eclipsing stars differ by 6.9%+/-0.8%, the temperatures differ by 9.2%+/-0.2%, and consequently the luminosities differ by 62%+/-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+/-0.003. In addition, we measure the rotation rate of the eclipsing stars to be 4.629+/-0.006 days; they rotate slightly faster than their 4.674 day 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.