"Chill out" originated on the east coast, NYC specifically and was a term used by heroin addicts who were going through heroin withdrawals. One of the many symptoms of heroin withdrawal is getting the chills and fellow junkies as a way to say see you later would tell each other to "chill out" meaning stay well, don't get sick or don't go into withdrawals from not having heroin.
See also "Dope Sick"
"I'm sick man, you got anything, I need something?" "No, I got nothing, chill out."