Absorption line systems detected in quasar spectra can be used to compare the value of the fine-structure constant, {alpha}, measured today on Earth with its value in distant galaxies. In recent years, some evidence has emerged of small temporal and also spatial variations of {alpha} on cosmological scales which may reach a fractional level of ~ 10 ppm (parts per million). To test these claims we are conducting a Large Program with the VLT UVES . We are obtaining high-resolution (R ~ 60000 and high signal-to-noise ratio (S/N ~ 100) UVES spectra calibrated specifically for this purpose. Here we analyse the first complete quasar spectrum from this Program, that of HE 2217-2818. We apply the Many Multiplet method to measure {alpha} in 5 absorption systems towards this quasar: zabs = 0.7866, 0.9424, 1.5558, 1.6279 and 1.6919. The most precise result is obtained for the absorber at zabs = 1.6919 where 3 Fe II transitions and Al II {lambda}1670 have high S/N and provide a wide range of sensitivities to {alpha}. The absorption profile is complex, with several very narrow features, and requires 32 velocity components to be fitted to the data. Our final result for the relative variation in {alpha} in this system is Delta{alpha}/{alpha} = +1.3 +/- 2.4stat +/- 1.0sys ppm. This is one of the tightest current bounds on {alpha} variation from an individual absorber. The absorbers towards quasar HE 2217-2818 reveal no evidence for variation in {alpha} at the 3 ppm precision level (1{sigma} confidence). If the recently reported 10 ppm dipolar variation of {alpha} across the sky were correct, the expectation at this sky position is (3.2-5.4) +/-1.7 ppm depending on dipole model used . Our constraint of Delta{alpha}/{alpha}=+1.3+/-2.4stat +/-1.0sys ppm is not inconsistent with this expectation.
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