Something that "burns a chill" would be a scenario or event that would also
kill a buzz or harsh a mellow. Such things include: loud noises, over-excited or un-chill people, running out of the means to be chill, eating the last
cookie, etc. "burning a chill" is just another saying in accordance to harshing a mellow or killing a buzz.
Quite simply, a chill burn is a buzz
kill.
"Hey
man why don't we get off our asses and go out and do
something fun?!?!"
"Dude, that would totally burn my chill"
"Spence, it's time to go
shopping with me; you promised!"
"Relax, brosephine, you're such a chill burn."