  We report on Chandra X-ray and Gemini-North near-infrared K-band observations
of the eclipsing accretion-powered millisecond X-ray pulsar SWIFT J1749.4-2807
in quiescence. Using the Chandra observation we derive a source position of
Right Ascencion: 17:49:31.73 and Declination:-28:08:05.08. The position is
accurate to 0.6" (90 per cent confidence). We find one source at a magnitude
K=18.44+-0.03 with a position fully consistent with the accurate Chandra X-ray
localization and a second source at K=19.2+-0.1 that falls close to the edge of
the error circle in the deep K-band images. The presence of a few weaker
sources as suggested by previous H-band observations presented in the
literature cannot the ruled out. There is marginal evidence that the brighter
of the these two sources is variable. Follow-up spectroscopy of this potential
counterpart will show if this source is the true counterpart to SWIFT
J1749.4-2807. If so, baring the presence of complicating effects such as
heating of the mass-donor star, it would allow for the mass of the neutron star
to be measured through the measurement of periodic radial velocity variations.
