When I chill with my immersion chiller I use the tap water first, that gets it down halfway - the hot water from the chiller empties into my washing machine.
Then when I cant get any more cooling power from the tap water, I put a pump on the immersion chiller and put the pump with the inlet and outlet in a round cooler of ice water. This recirculates very cold water through the chiller and works well to get it down to pitch temp - when that's done, I dump that into the washer too.
I do a load of laundry usually the next day.