The brightest southern quasar above redshift z = 1 , HE 0515 - 4414 , with its strong intervening metal absorption-line system at z _ { \text { \scriptsize abs } } = 1.1508 , provides a unique opportunity to precisely measure or limit relative variations in the fine-structure constant ( \Delta \alpha / \alpha ) . A variation of just \sim 3 parts per million ( ppm ) would produce detectable velocity shifts between its many strong metal transitions . Using new and archival observations from the Ultraviolet and Visual Echelle Spectrograph ( UVES ) we obtain an extremely high signal-to-noise ratio spectrum ( peaking at \textrm { S / N } \approx 250 pix ^ { -1 } ) . This provides the most precise measurement of \Delta \alpha / \alpha from a single absorption system to date , \Delta \alpha / \alpha = -1.42 \pm 0.55 _ { stat } \pm 0.65 _ { sys } ppm , comparable with the precision from previous , large samples of \sim 150 absorbers . The largest systematic error in all ( but one ) previous similar measurements , including the large samples , was long-range distortions in the wavelength calibration . These would add a \sim 2 ppm systematic error to our measurement and up to \sim 10 ppm to other measurements using Mg and Fe transitions . However , we corrected the UVES spectra using well-calibrated spectra of the same quasar from the High Accuracy Radial velocity Planet Searcher ( HARPS ) , leaving a residual 0.59 ppm systematic uncertainty , the largest contribution to our total systematic error . A similar approach , using short observations on future , well-calibrated spectrographs to correct existing , high S/N spectra , would efficiently enable a large sample of reliable \Delta \alpha / \alpha measurements . The high S/N UVES spectrum also provides insights into analysis difficulties , detector artifacts and systematic errors likely to arise from 25–40-m telescopes .