Statistical copolymers were prepared by the Ring Opening Metathesis coPolymerization (ROMP) of (Z)-5,5-dimethylcyclooct-1-ene and cis-cyclooctene. Subsequent hydrogenation yielded poly(ethylene-co-isobutylene) (PEIB) materials. The feed ratio of the comonomers controls the degree of branching and resulting thermal and mechanical properties of the PEIB samples. Oxidative degradation studies, conducted under accelerated in vitro conditions were used to assess and predict their long-term biostability. Relative to commercial poly(ether urethanes) and a structurally similar polyolefin, poly(ethylene-co-1-butylene), the PEIB samples showed much better oxidative resistance. The facile synthesis, improved stability, and excellent mechanical performance of these PEIB materials bode well for their use in biomedical applications that require long-term biostability.