We report a detection of the coherent distortion of faint galaxies arising from gravitational lensing by foreground structures. This `cosmic shear' is potentially the most direct measure of the mass power spectrum, as it is unaffected by poorly justified assumptions made concerning the biasing of the distribution. Our detection is based on an initial imaging study of 14 separated 8 Γ 16 arcmin 2 fields observed in good, homogeneous conditions with the prime focus EEV-CCD camera of the 4.2-m William Herschel Telescope. We detect an rms shear of 1.6 per cent in 8 Γ 8 arcmin 2 cells, with a significance of 3.4s . We carefully justify this detection by quantifying various systematic effects and carrying out extensive simulations of the recovery of the shear signal from artificial images defined according to measured instrument characteristics. We also verify our detection by computing the crosscorrelation between the shear in adjacent cells. Including (Gaussian) cosmic variance, we measure the shear variance to be 0X016 2 ^0X012 2 ^0X006 2 Y where these 1s errors correspond to statistical and systematic uncertainties, respectively. Our measurements are consistent with the predictions of cluster-normalized cold dark matter (CDM) models (within 1s ) but a Cosmic Background Explorer normalized standard cold dark matter model is ruled out at the 3.0s level. For the currently favoured LCDM model (with V m 0X3Y our measurement provides a normalization of the mass power spectrum of s 8 1X5 ^0X5Y fully consistent with that derived from cluster abundances. Our result demonstrates that groundbased telescopes can, with adequate care, be used to constrain the mass power spectrum on various scales. The present results are limited mainly by cosmic variance, which can be overcome in the near future with more observations.