The property is that both sets of alternate letters form valid English words.
ChAiNs - can, his
CoUnTeSs - cuts, ones
StAiNeD - sand, tie
ScHoOlEd - shoe, cold
PuRrInG - prig, urn
CoRnY - cry, on
So the answer is SpOiLeD - sold, pie
Today's brain teaser courtesy of Braingle.com.