We present an analysis of three archival Chandra observations of the black hole V4641 Sgr, performed during a decline into quiescence. The last two observations in the sequence can be modeled with a simple power-law. The first spectrum, however, is remarkably similar to spectra observed in Seyfert-2 active galactic nuclei, which arise through a combination of obscuration and reflection from distant material. This spectrum of V4641 Sgr can be fit extremely well with a model including partial-covering absorption and distant reflection. This model recovers a Gamma = 2 power-law incident spectrum, typical of black holes at low Eddington fractions. The implied geometry is plausible in a high-mass X-ray binary like V4641 Sgr, and may be as compelling as explanations invoking Doppler-split line pairs in a jet, and/or unusual Comptonization. We discuss potential implications and means of testing these models.