  Given $\Omega$ a bounded open subset of $\mathbb{R}^N$, we consider
nonnegative solutions to the singular semilinear elliptic equation
$-\Delta\,u\,=\,\frac{f}{u^{\beta}}$ in $H^1_{loc}(\Omega)$, under zero
Dirichlet boundary conditions. For $\beta>0$ and $f\in L^1(\Omega)$, we prove
that the solution is unique.
