We have determined an improved position for the luminous persistent neutron-star low-mass X-ray binary and atoll source GX 9+1 from archival Chandra X-ray Observatory data. The new position significantly differs from a previously published Chandra position for this source. Based on the revised X-ray position we have identified a new near-infrared (NIR) counterpart to GX 9+1 in Ks-band images obtained with the PANIC and FourStar cameras on the Magellan Baade Telescope. NIR spectra of this Ks=16.5+-0.1 mag star taken with the FIRE spectrograph on the Baade Telescope show a strong Br-gamma emission line, which is a clear signature that we discovered the true NIR counterpart to GX 9+1. The mass donor in GX 9+1 cannot be a late-type giant, as such a star would be brighter than the estimated absolute Ks magnitude of the NIR counterpart. The slope of the dereddened NIR spectrum is poorly constrained due to uncertainties in the column density N_H and NIR extinction. Considering the sources distance and X-ray luminosity, we argue that N_H likely lies near the high end of the previously suggested range. If this is indeed the case, the NIR spectrum is consistent with thermal emission from a heated accretion disk, possibly with a contribution from the secondary. In this respect, GX 9+1 is similar to other bright atolls and the Z sources whose NIR spectra do not show the slope that is expected for a dominant contribution from optically thin synchrotron emission from the inner regions of a jet.