  We report the discovery of a near-infrared (nIR) counterpart to the
persistent neutron-star low-mass X-ray binary 4U 1705-440, at a location
consistent with its recently determined Chandra X-ray position. The nIR source
is highly variable, with K_s-band magnitudes varying between 15.2 and 17.3 and
additional J- and H-band observations revealing color variations. A comparison
with contemporaneous X-ray monitoring observations shows that the nIR
brightness correlates well with X-ray flux and X-ray spectral state. We also
find possible indications for a change in the slope of the nIR/X-ray flux
relation between different X-ray states. We discuss and test various proposed
mechanisms for the nIR emission from neutron-star low-mass X-ray binaries and
conclude that the nIR emission in 4U 1705-440 is most likely dominated by X-ray
heating of the outer accretion disk and the secondary star.
