Best bet is to make sure that any oils left over from the extrusion process are removed with a detergent of some kind and then you can remove any oxidation by boiling for 10 minutes in enough water to cover it with a cup or two of WHITE VINEGAR not cider vinegar. It will come out looking like a shiny new penny.
Your wort will have the same effect as the vinegar boil, so if you brew often enough it will remain shiny. If you go along time between brew sessions, the chiller will oxidize some and you can just give it another vinegar boil. Some people just say put in the wort and it will remove the oxidation. I don't know about you, but I don't want any oxides of copper in my beer.
FWIW, if you ever see any green stuff anywhere on the copper, it's called verdigris, and it's a poison, so make sure to clean it off.