We previously reported Keck telescope observations suggesting a smaller value of the fine structure constant α at high redshift. New Very Large Telescope (VLT) data, probing a different direction in the Universe, shows an inverse evolution; α 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 σ level, in the direction right ascension 17.5 ± 0.9 h, declination -58 ± 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.