Deep photometry of the Small Magellanic Cloud ( SMC ) stellar periphery ( R =4° , 4.2 kpc ) is used to study its line-of-sight depth with red clump ( RC ) stars . The RC luminosity function is affected little by young ( \lesssim 1 Gyr ) blue-loop stars in these regions because their main-sequence counterparts are not observed in the color magnitude diagrams . The SMC ’ s eastern side is found to have a large line-of-sight depth ( \sim 23 kpc ) while the western side has a much shallower depth ( \sim 10 kpc ) , consistent with previous photographic plate photometry results . We use a model SMC RC luminosity function to deconvolve the observed RC magnitudes and construct the density function in distance for our fields . Three of the eastern fields show a distance bimodality with one component at the “ systemic ” \sim 67 kpc SMC distance and a second component at \sim 55 kpc . Our data are not reproduced well by the various extant Magellanic Cloud and Stream simulations . However , the models predict that the known H I Magellanic Bridge ( stretching from the SMC eastward towards the LMC ) has a decreasing distance with angle from the SMC and should be seen in both the gaseous and stellar components . From comparison with these models we conclude that the most likely explanation for our newly identified \sim 55 kpc stellar structure in the eastern SMC is a stellar counterpart of the H I Magellanic Bridge that was tidally stripped from the SMC \sim 200 Myr ago during a close encounter with the LMC . This discovery has important implications for microlensing surveys of the SMC .