This disclosure relates to golf balls having a cover layer 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 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 cover layer may have certain properties, such as a desirable flexural modulus value and a desirable Shore D hardness value, that further contribute to the golf ball having a high degree of scuff resistance.