We present estimates of the selection on and the heritability of a male secondary sexual weapon in a wild population: antler size in red deer. Male red deer with large antlers had increased lifetime breeding success, both before and after correcting for body size, generating a standardized selection gradient of 0.44 (+/- 0.18 SE). Despite substantial age- and environment-related variation, antler size was also heritable (heritability of antler mass = 0.33 +/- 0.12). However the observed selection did not generate an evolutionary response in antler size over the study period of nearly 30 years, and there was no evidence of a positive genetic correlation between antler size and fitness nor of a positive association between breeding values for antler size and fitness. Our results are consistent with the hypothesis that a heritable trait under directional selection will not evolve if associations between the measured trait and fitness are determined by environmental covariances: In red deer males, for example, both antler size and success in the fights for mates may be heavily dependent on an individual's nutritional state.