Abstract: A chlorinated rubber having a chlorine content of about 5 through about 50% by weight and a Mooney viscosity (ML.sub.1+4 at 100.degree. C.) of about 20 through about 150 is presented. This chlorinated rubber is derived from the chlorination of (i) a copolymer rubber of ethylene and 1-butene having a mol ratio of ethylene/1-butene of about 85/15 through about 95/5 or (ii) a copolymer rubber of ethylene 1-butene and 5-ethylidene-2-norbornene having a mol ratio of ethylene/1-butene of about 85/15 through about 95/5 and a content of the 5-ethylidene-2-norbornene of 20% by weight or less based on the weight of the copolymer. The incorporation of the chlorinated rubber into a polyvinyl chloride composition results in the remarkable improvement of the impact resistance and flexibility, both at a low temperature, of the polyvinyl chloride.