We measure the alignment of galaxy ellipticities in the local Universe over a range of scales using digitized photographic data from the {SuperCOSMOS} Sky Survey. We find for a magnitude cut of {bJ{\textless}20.5}, corresponding to a median galaxy redshift of z{~}0.1, and 2??106 galaxies, that the galaxy ellipticities exhibit a non-zero correlation over a range of scales between 1 and 100arcmin. We detect this correlation in two colours, {bJ} and R and, most significantly, in the cross-correlation between the two bands, which is less likely to be contaminated by systematics. In particular, we measure the variance of mean galaxy ellipticities, ??2(??), in square angular cells on the sky as a function of cell size and find that it lies in the range, 2??10- 4{\textgreater}=??2(??){\textgreater}{~}1??10-5 for cell side lengths of between 15{\textless}=??{\textless}=100arcmin. Considering the low median redshift of the galaxies in the sample and hence the relatively low effective cross-section for lensing of these galaxies by the large-scale structure of the Universe, we propose that we have detected an intrinsic alignment of galaxy ellipticities. We compare our results with recent analytical and numerical predictions made for intrinsic galaxy alignment and find good agreement. We discuss the importance of these results for measuring cosmic shear from upcoming shallow surveys (e.g. the Sloan Digital Sky Survey) and we outline how these measurements could possibly be used to constrain models of galaxy formation and/or measure the mass distribution in the local Universe.