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"Thing" isn't an obvious supernym for a "right".  The legal definition of a "thing" is narrower than "simply anything" and it varies not just by a language, but also by jurisdiction.

Any chose in action is associated with a specific kind of a right: a property right.   
 That's what makes it a "thing".  Somebody owns the chose in action.  For example, they owe someone else's debt.  It's difficult to collect it, one cannot hold such a thing in their hand (not until it is collected and not after it is collected), but it may still have a certain value and there's a procedure that lets one collect it: that procedure is the "action" in "chose in action".

Not every right is a property right.  I have a right to be silent - but there's no abstract thing I can point to and say "this is my silence and I own it."  I also cannot ask a court to enforce my right to be silent (to "collect" the right), therefore this right is not a property right and it is not a chose in action.