  In this letter we discuss the influence of a U(1) chemical potential $\mu$ on
the existence of Gribov copies in a U(1) theory at finite temperature $T$. We
show that the chemical potential conspires against the existence of Gribov
copies in the sense that it restricts the space of solutions of the consistency
equation for the gauge parameter. Explicit solutions are found for T=0, as
function of $\mu$. In the finite temperature case we find also a class of
solutions which satisfy the KMS boundary conditions in the euclidean time
direction, having also a vanishing behavior when $|\mathbf r|\to\infty$
