We previously reported Keck telescope observations suggesting a smaller value of the fine structure constant $\alpha$ at high redshift. New Very Large Telescope (VLT) data, probing a different direction in the Universe, shows an inverse evolution; $\alpha$ increases at high redshift. Although the pattern could be due to as yet undetected systematic effects, with the systematics as presently understood the combined data set fits a spatial dipole, significant at the $4.2\sigma$ level, in the direction right ascension $17.5\pm 0.9$ h, declination $-58\pm 9$ deg. The independent VLT and Keck samples give consistent dipole directions and amplitudes, as do high and low redshift samples. A search for systematics, using observations duplicated at both telescopes, reveals none so far which emulate this result.