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Observations of distant supernovae indicate that the Universe is now in a phase of accelerated expansion the physical cause of which is a mystery. Formally, this requires the inclusion of a term acting as a negative pressure in the equations of cosmic expansion, accounting for about 75 per cent of the total energy density in the Universe. The simplest option for this 'dark energy' corresponds to a 'cosmological constant', perhaps related to the quantum vacuum energy. Physically viable alternatives invoke either the presence of a scalar field with an evolving equation of state, or extensions of general relativity involving higher-order curvature terms or extra dimensions. Although they produce similar expansion rates, different models predict measurable differences in the growth rate of large-scale structure with cosmic time. A fingerprint of this growth is provided by coherent galaxy motions, which introduce a radial anisotropy in the clustering pattern reconstructed by galaxy redshift surveys. Here we report a measurement of this effect at a redshift of 0.8. Using a new survey of more than 10,000 faint galaxies, we measure the anisotropy parameter beta = 0.70 +/- 0.26, which corresponds to a growth rate of structure at that time of f = 0.91 +/- 0.36. This is consistent with the standard cosmological-constant model with low matter density and flat geometry, although the error bars are still too large to distinguish among alternative origins for the accelerated expansion. The correct origin could be determined with a further factor-of-ten increase in the sampled volume at similar redshift.