Dark matter direct detection experiments need to know the local phase space density of dark matter fdm(r,v,t) in order to derive dark matter particle properties. To date, calculations for fdm(r,v,t) have been based on simulations that model the dark matter alone. Here we include the influence of the baryonic matter. We find that a star/gas disc at high redshift (z~1) causes merging satellites to be preferentially dragged towards the disc plane. This results in an accreted dark matter disc that contributes ~0.25-1 times the non-rotating halo density at the Solar position. We discuss the impact of the dark disc on dark matter direct detection experiments, and how we might be able to detect it in future Galactic surveys.