  Over a one-dimensional Gorenstein local domain $R$, let $E$ be the
endomorphism ring of the maximal of $R$, viewed as a subring of the integral
closure $\overline R$. If there exist finitely generated $R$-modules $M$ and
$N$, neither of them free, whose tensor product is torsion-free, we show that
$E$ must be local with the same residue field as $R$.
