We observed six He-clump stars of the intermediate-age stellar cluster Gaia1 with the MIKE/MAGELLAN spectrograph. A possible extra-galactic origin of this cluster, recently discovered thanks to the first data release of the ESA Gaia mission, has been suggested, based on its orbital parameters. Abundances for Fe, {alpha}, proton- and neutron-capture elements have been obtained. We find no evidence of intrinsic abundance spreads. The iron abundance is solar ([FeI/H]=+0.00+/-0.01; {sigma}=0.03dex). All the other abundance ratios are generally solar-scaled, similar to the Galactic thin disk and open cluster stars of similar metallicity. The chemical composition of Gaia1 does not support an extra-galactic origin for this stellar cluster, which can be considered as a standard Galactic open cluster.