  Let $M^*(q)$ be the unique nonassociative finite simple Moufang loop
constructed over $GF(q)$. We prove that $Aut(M^*(2))$ is the Chevalley group
$G_2(2)$, by extending multiplicative automorphism of $M^*(2)$ into linear
automorphisms of the unique split octonion algebra over GF(2). Many of our
auxiliary results apply in the general case. In the course of the proof we show
that every element of a split octonion algebra can be written as a sum of two
elements of norm one.
