Copolymers of propylene and the polar monomer 6-tert-butyl-2-(1,1-dimethylhept-6-enyl)-4-methylphenol were obtained with racemic [1,1’-(dimethylsilylene)bis(eta5-4,5,6,7-tetrahydro-1-indenyl)]-zirconium dichloride and methylalumoxane activator. The copolymers contained from 1.3 to 5.5 wt % of phenolic units and exhibited high thermooxidative stability even after prolonged extraction with a mixture of refluxing (50:50) 2-propanol/cyclohexane. The initial polymerization rate, compared to that of homopolymerization of propylene, increased up to almost 6 times when the sterically hindered phenolic stabilizer monomer was added. A similar increase in activity was recorded when 2,6-di-tert-butylphenol was added during propylene polymerization. The activity enhancement was attributed to the ability of the phenolic stabilizer to function as a large weakly coordinating anion, which stabilizes the cationic polymerization center. The degree of microtacticity of the copolymer, isotactic triad mm > 0.96, was similar to that of isotactic polypropylene prepared by the same catalyst system. The dominating insertion mechanism was 1,2 addition with very low amounts of 1,3-addition irregularities. The produced copolymers exhibited lower melting points and crystallinities than polypropylene obtained under similar conditions. According to gel permeation chromatography, the copolymers had a narrow molecular weight distribution ranging from 1.9 to 2.1, which is close to those values characteristic for polymers produced by single-site catalysts.