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BG Ind is a well studied, bright, nearby binary consisting of a pair of Fstars in a 1.46-day orbit. We have discovered in the TESS lightcurve for TIC229804573 (aka BG Ind) a second eclipsing binary in the system with a 0.53-day.Our subsequent analyses of the recent TESS and archival ground-basedphotometric and radial velocity data, reveal that the two binaries aregravitationally bound in a 721-day period, moderately eccentric orbit. Wepresent the results of a joint spectro-photodynamical analysis of the eclipsetiming variation curves of both binaries based on TESS and ground-basedarchival data, the TESS lightcurve, archival radial velocity data and thespectral energy distribution, coupled with the use of PARSEC stellarisochrones. We confirm prior studies of BG Ind which found that the brighterbinary A consists of slightly evolved F-type stars with refined masses of 1.32and 1.43 $M_\odot$, and radii of 1.59 and 2.34 $R_\odot$. The previouslyunknown binary B has two less massive stars of 0.69 and 0.64 $M_\odot$ andradii of 0.64 and 0.61 $R_\odot$. Based on a number of different argumentswhich we discuss, we conclude that the three orbital planes are likely alignedto within 17$^\circ$.

BG Ind: the nearest doubly eclipsing, compact hierarchical quadruple system