As all four meiotic products give rise to sperm in males, female meiosis result in a single egg in most eukaryotes. Any genetic element with the potential to influence chromosome segregation, so that it is preferentially included in the egg, should therefore gain a transmission advantage; a process termed female meiotic drive. We are aware of two chromosomal components, centromeres and telomeres, which share the potential to influence chromosome movement during meioses and make the following predictions based on the presence of female meiotic drive: (1) centromere-binding proteins should experience rapid evolution as a result of a conflict between driving centromeres and the rest of the genome; and (2) segregation patterns should be skewed near centromeres and telomeres. To test these predictions, we first analyze the molecular evolution of seven centromere-binding proteins in nine divergent bird species. We find strong evidence for positive selection in two genes, lending support to the genomic conflict hypothesis. Then, to directly test for the presence of segregation distortion, we also investigate the transmission of approximately 9000 single-nucleotide polymorphisms in 197 chicken families. By simulating fair Mendelian meioses, we locate chromosomal regions with statistically significant transmission ratio distortion. One region is located near the centromere on chromosome 1 and a second region is located near the telomere on the p-arm of chromosome 1. Although these observations do not provide conclusive evidence in favour of the meiotic drive/genome conflict hypothesis, they do lend support to the hypothesis that centromeres and telomeres drive during female meioses in chicken.