No, it does not mean completely. It means "calm down". If something is boiling, you stop the boiling by cooling the liquid. That's what "chill out" means, cool down, or calm down, when one is upset and "boiling" with some emotion (anger, anxiety, enthusiasm, whatever extreme emotion it may be). "Chill out" is also meant to relax, as in just lie around and enjoy life, as opposed to being active. It's slang, only used in conversational speech, not formal writing unless in a quote or in quotation marks.
