1) A mixture of being chill and relaxing which can include listening to mellow music, watching TV, getting on facebook, taking a nap or simply laying down.
2) The much cooler way to say "take a chill pill." Similar to "calm down." Used when someone is freaking out for no good reason and causing others to feel stressed or when someone is acting like a dumbass.
"I'm going to chilax for a while before I go out tonight."
"Chilax, it's not like I wasn't going to pay you back."