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.
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