Three of the four possible structures for polymers formed from an achiral monomer through a single ROMP polymerization step have been prepared for a small collection of monomers. Trans,syndiotactic structures have been prepared through chain end control, cis,isotactic polymers have been prepared through enantiomorphic site control, and cis,syndiotactic polymers have been prepared through stereogenic metal control. Stereogenic metal control at the metal center as a means of forming syndiotactic polymers is virtually unknown. Synthesis of ROMP polymers with a regular structure that contain alternating enantiomers from a racemic mixture of monomers is a natural consequence of stereogenic metal control. Ruthenium catalysts do not display ROMP specificities analogous to those described here, perhaps since alkylidene isomers have not been observed for Ru catalysts and the barrier to rotation of the carbene in a generic NHC dichloride Ru catalyst has been calculated to be relatively low.