We calculate the potential of mean force of a pair of identical rodlike polyions, oriented in parallel, in 1:1 electrolyte solution. The polyions are modeled as infinite linear arrays of uniformly spaced monovalent charge sites. The analysis is accomplished within the framework of counterion condensation theory. The mean force between the polyions is repulsive for distances much less than the Debye length and for distances on the order of a Debye length. There is an intermediate range of distances, however, not small but less than the Debye length, where the polyions attract each other. The predominant cause of the effect is expansion ofthe condensation region into the space between the polyions, allowing condensed counterions to be shared with greatly enhanced translational entropy.