Global environmental change is expected to alter selection pressures in many biological systems(1-3), but the long-term molecular and life history data required to quantify changes in selection are rare(4). An unusual opportunity is afforded by three decades of individual-based data collected from a declining population of Antarctic fur seals in the South Atlantic. Here, climate change has reduced prey availability and caused a significant decline in seal birth weight. However, the mean age and size of females recruiting into the breeding population are increasing. We show that such females have significantly higher heterozygosity (a measure of within-individual genetic variation) than their non-recruiting siblings and their own mothers. Thus, breeding female heterozygosity has increased by 8.5% per generation over the last two decades. Nonetheless, as heterozygosity is not inherited from mothers to daughters, substantial heterozygote advantage is not transmitted from one generation to the next and the decreasing viability of homozygous individuals causes the population to decline. Our results provide compelling evidence that selection due to climate change is intensifying, with far-reaching consequences for demography as well as phenotypic and genetic variation.