We describe the results of a search for time variability of the fine struct
ure constant a using absorption systems in the spectra of distant quasars.
Three large optical data sets and two 21 cm and mm absorption systems provi
de four independent samples, spanning similar to 23% to 87% of the age of t
he universe. Each sample yields a smaller a in the past and the optical sam
ple shows a 4 sigma deviation: Delta alpha/alpha = -0.72 +/-0.18 x 10(-5) o
ver the redshift range 0.5 < z < 3.5. We find no systematic effects which c
an explain our results. The only potentially significant systematic effects
push Delta alpha/alpha towards positive values; i.e., our results would be
come more significant were we to correct for them.