Recent models of rotating massive stars including magnetic fields prove it difficult for the cores of single stars to retain enough angular momentum to produce a collapsar and gamma-ray burst. At low metallicity, even very massive stars may retain a massive hydrogen envelope due to the weakness of the stellar winds, posing an additional obstacle to the collapsar model. Here, we consider the evolution of massive, magnetic stars where rapid rotation induces almost chemically homogeneous evolution. We find that in this case, the requirements of the collapsar model are rather easily fulfilled if the metallicity is sufficiently small: 1) rapidly rotating helium stars are formed without the need to remove the hydrogen envelope, avoiding mass-loss induced spin-down. 2) Angular momentum transport from the helium core to hydrogen envelope by magnetic torques is insignificant. We demonstrate this by calculating evolutionary models of massive stars with various metallicities, and derive an upper metallicity limit for this scenario based on currently proposed mass loss rates. Our models also suggest the existence of a lower CO-core mass limit of about $10\,{M}_\odot$ – which relates to an initial mass of only about $20\,{M}_\odot$ within our scenario – for GRB production. We argue that the relative importance of the considered GRB progenitor channel, compared to any channel related to binary stars, may increase with decreasing metallicity, and that this channel might be the major path to GRBs from first stars.