The conductance of carbon-atom chains is found from first-principles c
alculations to vary in an oscillatory manner as the number of carbon a
toms is increased, with odd-numbered chains having a lower resistance
than even-numbered chains. This finding is explained in terms of the e
lectronic structure of the free chains and its modification by interac
tion with the metal electrodes: the critical factor is the density of
states at the Fermi level of the combined electrode-atomic-wire system
. Stronger electrode-atomic-wire coupling, i.e., shorter metal-carbon
distance, does not necessarily imply a higher conductance.