Chaotic Neutral doesn't necessarily mean "crazy", it just means amoral and self-centred (like Bronn in GoT). In the specific instance you mentioned, a CN character might do that, if the price was right and they weren't worried about the enemies it'd make them down the road.
AD&D did a poor job of explaining chaotic neutral.
In AD&D: “Chaotic neutral characters believe that there is no order to anything, including their own actions. With this as a guiding principle, they tend to follow whatever whim strikes them at the moment. Good and evil are irrelevant when making a decision. Chaotic neutral characters are extremely difficult to deal with. Such characters have been known to cheerfully and for no apparent purpose gamble away everything they have on the roll of a single die. They are almost totally unreliable. In fact, the only reliable thing about them is that they cannot be relied upon! This alignment is perhaps the most difficult to play. Lunatics and madmen tend toward chaotic neutral behavior.”
This isn't chaotic neutral, it's "chaotic stupid".
Comments
To me, a character who "acts like crazy and gives the eggs to the demon lord" is very much chaotic evil, not neutral.
So, no.
http://tvtropes.org/pmwiki/pmwiki.php/Main/ChaoticStupid
I like to think of chaotic neutral as not believing that actions are inherently good or evil. They are moral relativists.