When in doubt, consult the dictionary of youth vernacular: http://www.urbandictionary.com/define.php?term=No+Chill. The way I'd define it personally is that chill is the quality of not being easily fazed and implies a coolness. Zero chill is the lack of that and might mean a person can't take jokes and is quick to anger. (Though of course depending on region and context, the phrase could be used differently)

Actually now that I look at the context again, and found a more specific term: http://www.urbandictionary.com/define.php?term=Zero+chill, it seems it just means not caring/being reckless, as in the first definition in the link above. These double meanings...