Long-duration gamma-ray bursts are associated with the explosions of massive stars(1) and are accordingly expected to reside in star-forming regions with molecular gas (the fuel for star formation). Previous searches for carbon monoxide (CO), a tracer of molecular gas, in burst host galaxies did not detect any emission(2-4). Molecules have been detected as absorption in the spectra of gamma-ray burst afterglows, and the molecular gas is similar to the translucent or diffuse molecular clouds of the Milky Way(5,6). Absorption lines probe the interstellar medium only along the line of sight, so it is not clear whether the molecular gas represents the general properties of the regions where the bursts occur. Here we report spatially resolved observations of CO line emission and millimetre-wavelength continuum emission in two galaxies hosting gamma-ray bursts. The bursts happened in regions rich in dust, but not particularly rich in molecular gas. The ratio of molecular gas to dust (<9-14) is significantly lower than in star-forming regions of the Milky Way and nearby star-forming galaxies, suggesting that much of the dense gas where stars form has been dissipated by other massive stars.