  Crossings of energy bands in solids that are not pinned at symmetry points in
the Brillouin zone and yet cannot be removed by perturbations are thought to be
conditioned on the presence of a nonsymmorphic symmetry. In this Letter we show
that such band crossings can actually appear also in a symmorphic crystal. A
study of a class of tight-binding multiband one-dimensional lattice models of
spinful electrons reveals that chiral, time-reversal and site-mirror symmetries
are suffcient to produce such movable but not removable band degeneracies.
