A Chaotic Neutral may IC apply to one faction ?

Any alignment can apply to any faction, but bear in mind it will be much more difficult to get into a faction if your alignment is far removed from the norm of the faction.

Anything is -possible-, but, for example, a CE member of the Society would have a harder time getting in than a NG one.

(And be sure to know what kind of NPCs are in the faction - for example, paladins!)

The applications sticky/announcement in Information for New Players includes recommended alignments, classes, etc.