  We consider a one-dimensional charge density wave (CDW) insulator formed by
Umklapp processes in a quarter-filled band. The spectrum of the model consists
of gapless, uncharged excitations carrying spin $\pm 1/2$ (spinons) and gapped,
spinless excitations carrying charge $\pm e/2$ (solitons and antisolitons). We
calculate the low-energy behaviour of the single-electron Green's function at
zero temperature. The spectral function exhibits a rather featureless
scattering continuum of two solitons and many spinons. The theory predicts that
the gap observed by Angle Resolved Photoemission (ARPES) is twice the
activation gap in the dc conductivity. We comment on possible applications to
${\rm PrBa_2Cu_3O_7}$ and to the Bechgaard salts.
