This is an Americanism from the mid-70s meaning to relax. As the answer above suggests, the idea behind it is that you are avoiding any 'heat' or excitement and staying 'cool'. I suspect the 'out' element might be connected with the use of drugs to achieve the effect, in the sense that you are 'out of it', as it were!
I wouldn't dream of arguing with Quizmonster, but I was once told that it was connected with drug taking. Specifically, amphetamines which raise the body temperature quite considerably. The cure is to lie the person down in a cool place and replace water in the body, i.e. chill out.
Thanks for that, Grunty. I did see a likely drugs connection, as I suggested above, but I'm grateful for the far more specific explanation of the 'chill' element you have provided. I think I'll combine both our responses and use them next time the question comes up! Cheers