According to Mendel's second law, chromosomes segregate randomly in meiosis. Non-random segregation is primarily known for cases of selfish meiotic drive in females, in which particular alleles bias their own transmission into the oocyte. Here we report a rare example of unselfish meiotic drive for crossover inheritance in the clonal raider ant, Ooceraea biroi, in which both alleles are co-inherited at all loci across the entire genome. This species produces diploid offspring parthenogenetically via fusion of two haploid nuclei from the same meiosis. This process should cause rapid genotypic degeneration due to loss of heterozygosity, which results if crossover recombination is followed by random (Mendelian) segregation of chromosomes. However, by comparing whole genomes of mothers and daughters, we show that loss of heterozygosity is exceedingly rare, raising the possibility that crossovers are infrequent or absent in O. biroi meiosis. Using a combination of cytology and whole-genome sequencing, we show that crossover recombination is, in fact, common but that loss of heterozygosity is avoided because crossover products are faithfully co-inherited. This results from a programmed violation of Mendel's law of segregation, such that crossover products segregate together rather than randomly. This discovery highlights an extreme example of cellular 'memory' of crossovers, which could be a common yet cryptic feature of chromosomal segregation.