Abstract We report the detection of the CO(3-2) emission line from the host galaxy of gamma-ray burst (GRB) 080207 at z = 2.086. This is the first detection of molecular gas in emission from a GRB host galaxy beyond redshift 1. We find this galaxy to be rich in molecular gas with a mass of $1.1 \times 10^{11}\,\rm M_{{\odot }}$ assuming αCO = 4.36 $\rm M_{{\odot }}\,(\rm K\,km\,s^{-1}\,pc^2)^{-1}$. The molecular gas mass fraction of the galaxy is ∼0.5, typical of star-forming galaxies (SFGs) with similar stellar masses and redshifts. With an $\rm SFR_{FIR}$ of 260 $\rm M_{{\odot }}\,yr^{-1}$, we measure a molecular gas depletion time-scale of 0.43 Gyr, near the peak of the depletion time-scale distribution of SFGs at similar redshifts. Our findings are therefore in contradiction with the proposed molecular gas deficiency in GRB host galaxies. We argue that the reported molecular gas deficiency for GRB hosts could be the artefact of improper comparisons or neglecting the effect of the typical low metallicities of GRB hosts on the CO-to-molecular-gas conversion factor. We also compare the kinematics of the CO(3-2) emission line to that of the H α emission line from the host galaxy. We find the H α emission to have contributions from two separate components, a narrow and a broad one. The narrow component matches the CO emission well in velocity space. The broad component, with a full width at half-maximum of ∼1100 $\rm km\,s^{-1}$, is separated by +390 $\rm km\,s^{-1}$ in velocity space from the narrow component. We speculate this broad component to be associated with a powerful outflow in the host galaxy or in an interacting system.