  As established by scanning tunneling microscopy (STM) cleaved surfaces of the
high temperature superconductor YBa$_2$Cu$_2$O$_{7-\delta}$ develop charge
density wave (CDW) modulations in the one-dimensional (1D) CuO chains. At the
same time, no signatures of the CDW have been reported in the spectral function
of the chain band previously studied by photoemission. We use soft X-ray angle
resolved photoemission (SX-ARPES) to detect a chain-derived surface band that
had not been detected in previous work. The $2k_\textup{F}$ for the new surface
band is found to be 0.55\,\AA$^{-1}$, which matches the wave vector of the CDW
observed in direct space by STM. This reveals the relevance of the Fermi
surface nesting for the formation of CDWs in the CuO chains in
YBa$_2$Cu$_2$O$_{7-\delta}$. In agreement with the short range nature of the
CDW order the newly detected surface band exhibits a pseudogap, whose energy
scale also corresponds to that observed by STM.
