"Hoo-Boy! Now I've heard it all! And there was Genghis Khan. And Nero. Throughout history cheap punks have tried to make themselves leaders. But in spite of their titles, they were still cheap punks!"
A sort of "Heroic Rebel", these are characters who do believe in doing good and set out to do the right thing, but also believe that the law gets in the way of doing the right thing and as such deliberately operate outside of authority and are usually either contemptuous of or distrustful of authority. Chaotic Good characters will only work with authority figures if absolutely necessary and are much more comfortable working outside of it and fighting evil on their own terms. Basically they're more "screw the rules" as opposed to Neutral Good characters, who don't care if they happen to break the rules but also don't set out to do so. It's also worth mentioning that Chaotic Good characters tend to be just a bit more prone to ruthless behavior than other Good characters.