Abstract We use Hubble Space Telescope (HST) imaging and near-infrared spectroscopy from Keck/MOSFIRE to study the sub-structure around the progenitor of a Milky Way-mass galaxy in the Hubble Frontier Fields (HFF). Specifically, we study an $r_e = 40^{+70}_{-30}$pc, M⋆ ∼ 108.2M⊙ rest-frame ultra-violet luminous “clump” at a projected distance of ∼100 pc from a M⋆ ∼ 109.8M⊙ galaxy at z = 2.36 with a magnification μ = 5.21. We measure the star formation history of the clump and galaxy by jointly modeling the broadband spectral energy distribution from HST photometry and Hα from MOSFIRE spectroscopy. Given our inferred properties (e.g., mass, metallicity, dust) of the clump and galaxy, we explore scenarios in which the clump formed in-situ (e.g., a star forming complex) or ex-situ (e.g., a dwarf galaxy being accreted). If it formed in-situ, we conclude that the clump is likely a single entity as opposed to a aggregation of smaller star clusters, making it one of the most dense star clusters cataloged. If it formed ex-situ, then we are witnessing an accretion event with a 1:40 stellar mass ratio. However, our data alone are not informative enough to distinguish between in-situ and ex-situ scenarios to a high level of significance. We posit that the addition of high-fidelity metallicity information, such as [O iii]4363Å, which can be detected at modest S/N with only a few hours of JWST/NIRSpec time, may be a powerful discriminant. We suggest that studying larger samples of moderately lensed sub-structures across cosmic time can provide unique insight into the hierarchical formation of galaxies like the Milky Way.