A Faint Near-Infrared Counterpart to the AXP 1E 2259+58.6We present near-infrared and optical observations of the field of the Anomalous X-ray Pulsar 1E 2259+58.6 taken with the Keck telescope. We derive a subarcsecond Chandra position and tie it to our optical reference frame using other stars in the field. We find a very faint source, K(s) = 21.7 +/- 0.2 mag, with a position coincident with the Chandra position. We argue that this is the counterpart. In the J, I, and R bands, we derive (two sigma) limits of 23.8, 25.6 and 26.4mag, respectively. As with 4U 0142+61, for which a similarly faint counterpart was found, our results are inconsistent with models in which the source is powered by accretion from a disk. The only model that is not inconsistent, appears to be that in which 1E 2259+58.6 is a magnetar.