We demonstrate the existence of a class of nontopological fermion string solutions. The fermion configurations exist because of a nontrivial coupling between the fermions and a real scalar field, and their long, thin regions of false vacuum are supported against collapse by the pressure of massless particles trapped in the interior, rather than by the supporting pressure given by Pauli's exclusion principle in white dwarfs and neutron stars. Our solutions, even with angular momentum, appear unstable to perturbations in the scalar fields.