When we really think about the fact that all of our ethical theories are based on arbitrary axioms, suddenly the teeth to ethics have a deep, serious problem.
The only argument we have at that point is that the axioms "feel" correct, and I have no problem with this basis, I consider myself someone with strong ethical viewpoints. However, when the foundation of ethics is based on feel, then there are serious problems, because it stands to reason that folks who have a different feel are entirely justified in their ethical standards (assuming good-faith and good reasoning).
At that point, we have the problem that almost every ethical theory (I would argue the concept of ethics), must be universalizable. That is, if something is wrong for me, it should be wrong for someone else in my position (not necessarily everyone). This is completely impossible when ethics are ultimately based on feel.
Now, Chompsky here is basically saying, come on, we have innate instinctual ethical views. I generally agree with him, but it ultimately doesn't matter. If ethical theory is simply instinctual, the same meta-ethical problem exists, it's just that the founding axiom that most folks will have is that the "normal" ethical view is the "correct" view... it's a fine axiom, we needn't argue about it, but it's still arbitrary, and effectively amounts to might makes right.