A systematic theory is presented for the prediction of oxygen migration near a 60° dislocation and for the resulting retardation of dislocation motion. Quantitative predictions are based on the solution of the macroscopic equation for transport of oxygen in the elastic stress field created by the dislocation. The link between the microscopic dynamics of interstitial oxygen within the diamond lattice and macroscopic transport is established by a constitutive model for the dependence of the drift velocity band diffusivity of oxygen on the elastic interaction of oxygen atoms and dislocations and on temperature. The transport equation is solved numerically assuming that the dislocation core is fully saturated with oxygen. The drag force on the gliding dislocation caused by the surrounding oxygen is computed from linear elasticity theory, combined with the phenomenological model of Alexander and Haasen [Solid State Phys.22, 27 (1968)] for the dependence on the applied stress of the velocity of a dislocation in pure silicon. The predicted dependence of the dislocation velocity on the applied stress at specific temperatures and oxygen concentrations is in qualitative agreement with the experimental data of Imai and Sumino [Philos. Mag. A47, 599 (1983)].