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Using the High Resolution Camera onboard the Chandra X-ray Observatory, we have measured an accurate position for the bright persistent neutron-star X-ray binary and atoll source GX 3+1. At a location that is consistent with this new position we have discovered the near-infrared (NIR) counterpart to GX 3+1 in images taken with the PANIC and FourStar cameras on the Magellan Baade Telescope. The identification of this K_s=15.8+-0.1 mag star as the counterpart is based on the presence of a Br-gamma emission line in a NIR spectrum taken with the FIRE spectrograph on the Baade Telescope. The absolute magnitude derived from the best available distance estimate to GX 3+1 indicates that the mass donor in the system is not a late-type giant. We find that the NIR light in GX 3+1 is likely dominated by the contribution from a heated outer accretion disk. This is similar to what has been found for the NIR flux from the brighter class of Z sources, but unlike the behavior of atolls fainter (Lx ~ 1e36 to 1e37 erg/s) than GX 3+1, where optically-thin synchrotron emission from a jet probably dominates the NIR flux.
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