The performance expected from a galaxy survey to be carried out withGAIA, the GAIA Galaxy Survey, is outlined. From a statistical modelof galaxy number density, size and surface brightness distribution,and from detailed numerical simulations based on real images, it isconservatively estimated that GAIA would be able to detect and observeabout 3 million galaxies brighter than V ≅ 17 and to providemulti-colour and multi-epoch broad-band photometry of these with anend-of-mission angular resolution of ≅0.35 arcsec and aphotometric accuracy of ≅0.2 mag/arsec2 atμV=20 mag/arsec2. The substantial scientific case for performing such a surveyand the additional efforts required in terms of mission preparation,operations and telemetry are also discussed.