ESS will be a premier neutron source facility. Unprecedented neutron beam intensities are ensured by spallation reactions of a 5 MW, 2.0 GeV proton beam impinging on a tungsten target equipped with advanced moderators. The work presented here aims at investigating possibilities for installing an ultra cold neutron (UCN) source at the ESS. One consequence of using the recently proposed flat moderators is that they take up less space than the moderators originally foreseen and thus leave more freedom to design a UCN source, close to the spallation hotspot. One of the options studied is to place a large 4He UCN source in a through-going tube which penetrates the shielding below the target. First calculations of neutron flux available for UCN production are given, along with heat-load estimates. It is estimated that the flux can give rise to a UCN production at a rate of up to 1.5 ⋅ 108 UCN/s. A production in this range potentially allows for a number of UCN experiments to be carried out at unprecedented precision, including, for example, quantum gravitational spectroscopy with UCNs which rely on high phase-space density.