  We study the energetics, the electronic structure, and the ballistic
transport of an infinite Au monatomic chain with an adsorbed CO molecule. We
find that the bridge adsorption site is energetically favored with respect to
the atop site, both at the equilibrium Au-Au spacing of the chain and at larger
spacings. Instead, a substitutional configuration requires a very elongated
Au-Au bond, well above the rupture distance of the pristine Au chain. The
electronic structure properties can be described by the Blyholder model, which
involves the formation of bonding/antibonding pairs of 5{\sigma} and 2{\pi}*
states through the hybridization between molecular levels of CO and metallic
states of the chain. In the atop geometry, we find an almost vanishing
conductance due to the 5{\sigma} antibonding states giving rise to a Fano-like
destructive interference close to the Fermi energy. In the bridge geometry,
instead, the same states are shifted to higher energies and the conductance
reduction with respect to pristine Au chain is much smaller. We also examine
the effects of strain on the ballistic transport, finding opposite behaviors
for the atop and bridge conductances. Only the bridge geometry shows a strain
dependence compatible with the experimental conductance traces.
