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 dataset fits a spatial dipole, significant at the 4.2-sigma level, in the direction right ascension 17.5 +/- 0.9 hours, declination -58 +/- 9 degrees. 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. \\ ( http://arxiv.org/abs/1008.3907 ,  234kb)