See, I'm a little confused. We all agree that Jayne is chaotic neutral because he betrays the group. Yes? Does anyone disagree with that? Would anyone put Jayne's alignment as something else?
So, what about Han Solo says Chaotic Neutral? He doesn't betray anyone. He's self interested, sure, but, that's just neutral. He doesn't do anything on a whim that I can think of.
This, in my view is one of the major problems with the 9-alignment system as traditionally presented in D&D. The difference between Chaotic and Neutral with respect to Law and Chaos is simply a matter of degree, and the line between them is not particularly bright. Sure, we can probably all agree that betraying one’s allies falls on the Chaotic side of the line, but does one betrayal make a self-interest les character Chaotic Neutral? Can a character be considered Chaotic Neutral if they haven’t betrayed their allies? And while we’re at it, isn’t self interest a characteristic of evil too? What can a self-interested character get away with doing before crossing the line from Neutral to Evil?
This is why I prefer to define Chaotic as not simply valuing their own individual freedom, but being ideologically opposed to Law. A Chaotic character is not merely an individualist, but an anarchist. Or a libertarian, I suppose. They fall on the far bottom portion of the political compass, is my point. Just as obeying laws doesn’t necessarily make one Lawful, breaking them doesn’t necessarily make one Chaotic. Law and Chaos are strong ideological stances, and Neutrality is merely the lack of a stance.
Now, if Law is roughly analogous to Authoritarianism and Chaos to Libertarianism, I like to map Good and Evil to Altruism and Egoism respectively. A Good character seeks to do the most good for others regardless of the cost to themselves, and an Evil character acts in their own self-interest regardless of the harm it may cause others. Neutrality on this spectrum is likewise defined by not taking a stance. The ethically neutral character does not knowingly harm others for their own benefit, but nor do they go out of their way to help others.
Personally, I would say Jayne’s willingness to betray his allies doesn’t make him Chaotic (though his opposition to the Authoritarian government certainly does that). It makes him Evil. Han, on the other hand, he starts out New Hope skirting the line between Chaotic Neutral and Chaotic Evil (leaning towards Evil when he shot first, but towards Neutral after the edit), and by the end of the film has come around to Chaotic Good. And he pretty much remains Chaotic Good for the rest of the trilogy.