  Let $k$ be a number field, suppose that $B$ is a central simple division
algebra over $k$, and choose any maximal order $\mathcal{D}$ of $B$. The object
of this paper is to show that the group $\mathcal{D}_S^*$ of $S$-units of $B$
is generated by elements of small height once $S$ contains an explicit finite
set of places of $k$. This generalizes a theorem of H.\ W.\ Lenstra Jr., who
proved such a result when $B = k$. Our height bound is an explicit function of
the number field and the discriminant of a maximal order in $B$ used to define
its $S$-units.
