Run a mixture of hot water and Oxiclean or PBW through the chiller for a while. If you want to try scrubbing the inside, try this:
Using compressed air or water pressure, push a string through the chiller. Attach a piece of wet cloth to the string. Attach another length of string to the first string where the cloth is attached. Pull the cloth through the chiller, rinse and pull the cloth back through the other direction. For a little more abrasive action you could put some baking soda on the cloth.