Is a polynomial group law on $mathbb{R}^n$ automatically nilpotent?

I was told that a polynomial group law on (all of) $mathbb{R}^n$ gives automatically a nilpotent (Lie, of course) group.

Is it true? Where can I find a proof?

A counterexample for open subsets of $mathbb{R}^n$ is furnished by the halfplane with the $ax+b$ law.