High-velocity galactic outflows, driven by intense bursts of star formation and black hole accretion, are invoked by current theories of galaxy formation to terminate star formation in the most massive galaxies and to deposit heavy elements in the intergalactic medium. From existing observational evidence on high-redshift galaxies, it is unclear whether such outflows are localized to regions of intense star formation just a few kiloparsecs in extent, or whether they instead have a significant impact on the entire galaxy and its surroundings. Here we present two-dimensional spectroscopy of a star-forming galaxy at redshift z=3.09 (seen 11.5 Gyr ago, when the Universe was 20 per cent of its current age): its spatially extended Ly-alpha emission appears to be absorbed by HI in a foreground screen covering the entire galaxy, with a lateral extent of at least 100 kpc and remarkable velocity coherence. It was plausibly ejected from the galaxy during a starburst several 1E8 yr earlier and has subsequently swept up gas from the surrounding intergalactic medium and cooled. This demonstrates the galaxy-wide impact of high-redshift superwinds.