We seek to determine whether the late-type star 2MASS J12354893-3950245 (2M1235-39) is a member of the TW Hya Association (TWA), a hypothesis suggested by its association with a bright X-ray source detected serendipitously by ROSAT and XMM-Newton and its (∼3') proximity to the well-studied (A+M binary) system HR 4796. We used optical spectroscopy to establish the Li and Hα line strengths of 2M1235-39, and determined its proper motion via optical imaging. We also considered its X-ray and near-IR fluxes relative to the M star HR 4796B. The optical spectrum of 2M1235-39 displays strong Li absorption and Hα emission (equivalent widths of 630mÅ and -6.7Å, respectively). Comparison of the spectrum with that of a nearby field star, along with the DENIS catalog IJK magnitudes, indicates the spectral type of 2M1235-39 is M4.5. We measure a proper motion for 2M1235-39 that agrees, within the errors, with that of HR 4796. The Li absorption and Hα emission line strengths of 2M1235-39, its near-IR and X-ray fluxes, and its proper motion all indicate that 2M1235-39 is a TWA member. Most likely this star is a wide (13500AU) separation, low-mass, tertiary component of the HR 4796 system.