Herein, we report the synthesis of polyesters via the alternating copolymerization of epoxides and cis-5-norbornene-endo-2,3-dicarboxylic anhydride (NB). The polymers are demonstrated to be of perfectly alternating structure with monomodal peak distributions and low polydispersity indexes. We demonstrate that these polyesters can be functionalized using thiol–ene and tetrazine click chemistry to form polymers with alternating functionality. Furthermore, we show that these polymers can be made thermally responsive, and can even be crosslinked when mixed with Grubbs’ catalyst.