Global warming has shifted phenological traits in many species, but whether species are able to track further increasing temperatures depends on the fitness consequences of additional shifts in phenological traits. To test this, we measured phenology and fitness of great tits ( Parus major ) with genotypes for extremely early and late egg lay dates, obtained from a genomic selection experiment. Females with early genotypes advanced lay dates relative to females with late genotypes, but not relative to nonselected females. Females with early and late genotypes did not differ in the number of fledglings produced, in line with the weak effect of lay date on the number of fledglings produced by nonselected females in the years of the experiment. Our study is the first application of genomic selection in the wild and led to an asymmetric phenotypic response that indicates the presence of constraints toward early, but not late, lay dates.