This disclosure relates to golf balls made from a crosslinked thermoplastic polyurethane elastomer. The crosslinked thermoplastic polyurethane elastomer includes crosslinks located in the hard segments, where the crosslinks being the reaction product of unsaturated bonds located in the hard segments as catalyzed by a free radical initiator. The crosslinks may be formed from an unsaturated diol as a chain extender. The unsaturated diol may be trimethylolpropane monoallylether (TMPME). The golf ball may include the crosslinked thermoplastic polyurethane elastomer in the cover layer, in which case the cover layer may exhibit a high degree of scuff resistance.