To tell somebody to 'Chillax' is like telling somebody to chill and relax at the same time. This is often used when trying to imply that you did not mean to cause offense and you were just joking about.
Person A: What the hell man! Why would you do something like that?
Person B: Woah, just chillax! it was only a joke
a stupid word that is used to describe the act of chilling out and relaxing at the same time, often used by morons who claim that is "their word" and that they, "came up with it"