Recent observations have revealed that starburst galaxies can drive molecular gas outflows through stellar radiation pressure. Molecular gas is the phase of the interstellar medium from which stars form, so these outflows curtail stellar mass growth in galaxies. Previously known outflows, however, involve small fractions of the total molecular gas content and are restricted to sub-kiloparsec scales. It is also apparent that input from active galactic nuclei is in at least some cases dynamically important, so pure stellar feedback has been considered incapable of aggressively terminating star formation on galactic scales. Extraplanar molecular gas has been detected in the archetype starburst galaxy M82, but so far there has been no evidence that starbursts can propel significant quantities of cold molecular gas to the same galactocentric radius (~10 kpc) as the warmer gas traced by metal absorbers. Here we report observations of molecular gas in a compact (effective radius 100 pc) massive starburst galaxy at z=0.7, which is known to drive a fast outflow of ionized gas. We find that 35 per cent of the total molecular gas is spatially extended on a scale of approximately 10 kpc, and one third of this has a velocity of up to 1000 km/s. The kinetic energy associated with this high-velocity component is consistent with the momentum flux available from stellar radiation pressure. This result demonstrates that nuclear bursts of star formation are capable of ejecting large amounts of cold gas from the central regions of galaxies, thereby strongly affecting their evolution.
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