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We report the discovery in $TESS$ Sectors 3 and 4 of a compact triply eclipsing triple star system. TIC 209409435 is a previously unknown eclipsing binary with a period of 5.717 days, and the presence of a third star in an outer eccentric orbit of 121.872 day period was found from two sets of third-body eclipses and from eclipse timing variations. The latter exhibit signatures of strong 3rd-body perturbations. After the discovery, we obtained follow-up ground-based photometric observations of several binary eclipses as well as another of the third-body eclipses. We carried out comprehensive analyses, including the simultaneous photodynamical modelling of $TESS$ and ground-based lightcurves (including both archival WASP data, and our own follow-up measurements), as well as eclipse timing variation curves. Also, we have included in the simultaneous fits multiple star spectral energy distribution data and theoretical PARSEC stellar isochrones. We find that the inner binary consists of near twin stars of mass 0.90 $M_\odot$ and radius 0.88 $R_\odot$. The third star is just 9% more massive and 18% larger in radius. The inner binary has a rather small eccentricity while the outer orbit has $e = 0.40$. The inner binary and outer orbit have inclination angles within 0.1$^\circ$ and 0.2$^\circ$ of 90$^\circ$, respectively. The mutual inclination angle is $\lesssim 1/4^\circ$. All of these results were obtained without radial velocity observations.