What causes the green ring around an egg yolk when you chill a hard-boiled egg?
That's sulfur, and it's not caused by chilling. It's caused by overcooking the egg.
Actually, if you really want to get scientific, the green ring is caused by hydrogen in the egg white binding with sulfur in the egg yolk. It's harmless, but it is unsightly.
Cooking the eggs more gently keeps it from happening. I think people get confused by the term "hard-boiled" egg because they think it means boiling the eggs hard. I usually use the term "hard-cooked" to get away from that notion.
The method I use is to put the eggs in the pan so that they are covered by cold water. Put the pan on the stove and just bring it to a rolling boil. Cover the pan, turn off the heat and let the eggs stand in hot water for 17 to 18 minutes (it may take 20 minutes for extra-large eggs).
Then rinse the eggs under cold water, or put them in ice water to cool them using less water.
That method should keep you from turning green over your eggs.