An aircraft air conditioning system includes an air conditioning unit for the production of air conditioning air, which unit is connected to a pack air line, a recirculation air line adapted to be flown through with recirculation air and a mixing chamber, which is connected to the pack air line and the recirculation air line. An inlet line is connected to a connection on the aircraft for an aircraft-external air production unit and opens into the pack air line connecting the air conditioning unit to the mixing chamber. An air conditioning air line branches off from the pack air line between an opening point of the inlet line into the pack air line and the mixing chamber and is connectable to an aircraft area to be cooled.