We describe the results of a search for time variability of the fine structure constant \alpha using absorption systems in the spectra of distant quasars . Three large optical datasets and two 21cm/mm absorption systems provide four independent samples , spanning \sim 23 % to 87 % of the age of the universe . Each sample yields a smaller \alpha in the past and the optical sample shows a 4 \sigma deviation : \Delta \alpha / \alpha = -0.72 \pm 0.18 \times 10 ^ { -5 } over the redshift range 0.5 < z < 3.5 . We find no systematic effects which can explain our results . The only potentially significant systematic effects push \Delta \alpha / \alpha towards positive values , i.e . our results would become more significant were we to correct for them .