Hmm, I don't know what kind of environment you would keep your copper chiller in for it to turn green. I know it can/will happen if stored incorrectly. However, I've been using copper as a chiller for a number of years.. many of those years have seen no brewing.. and it NEVER turns green. It does get a dusky looking oxide on it.. but, far from green.
If there are any fears about it, soak it in a mild acetic bath like vinegar and the copper will be "new penny" clean. However, after you use it, the oxide will return. As long as you rinse the outside well and store it dry, you should never see a green oxide. The dusky/blackish oxide, which is very thin, will cause no troubles. It'll be the same color as a "not new" penny.