Context. The first Gaia Data Release (DR1) significantly improved the previously available proper motions for the majority of the Tycho-2 stars. Aims. We wish to detect runaway stars using Gaia DR1 proper motions and compare our results with previous searches. Methods. Runaway O stars and BA supergiants were detected using a 2D proper motion method. The sample was selected using Simbad, spectra from our GOSSS project, literature spectral types, and photometry processed using the code CHORIZOS. Results. We detect 76 runaway stars, 17 (possibly 19) of them with no prior identification as such, with an estimated detection rate of approximately one half of the real runaway fraction. An age effect appears to be present, with objects of spectral subtype B1 and later having traveled for longer distances than runaways of earlier subtypes. We also tentatively propose that the fraction of runaways is lower among BA supergiants that among O stars, but further studies using future Gaia data releases are needed to confirm this. The frequency of fast rotators is high among runaway O stars, which indicates that a significant fraction of them (and possibly the majority) is produced in supernova explosions.