  We argue that the results of recent scanning tunneling microscopy,
angle-resolved photoemission and infrared spectroscopy experiments on the CuO
chains of YBa$_2$Cu$_3$O$_{6+x}$ are consistently explained within a proximity
model by the interplay of a coherent chain-plane and an incoherent interchain
coupling. We show that the CuO$_2$ planes act as an ohmic heat bath for the
electronic degrees of freedom in the chains which induces a substantial quantum
dissipation. Below the planar $T_c$, charge excitations in the chains acquire a
universal superconducting gap whose phase and magnitude are momentum dependent.
We predict that the magnitude of this gap varies non-monotonically with the
hole concentration in the chains.
