Polyploidy is a major driver of evolutionary change. Autopolyploids, which arise by within-species whole-genome duplication, carry multiple nearly identical copies of each chromosome. This presents an existential challenge to sexual reproduction. Meiotic chromosome segregation requires formation of DNA crossovers (COs) between two homologous chromosomes. How can this outcome be achieved when more than two essentially equivalent partners are available? We addressed this question by comparing diploid, neo-autotetraploid, and established autotetraploid Arabidopsis arenosa using new approaches for analysis of meiotic CO patterns in polyploids. We discover that crossover interference, the classical process responsible for patterning of COs in diploid meiosis, is defective in the neo-autotetraploid but robust in the established autotetraploid. The presented findings suggest that, initially, diploid-like interference fails to act effectively on multivalent pairing and accompanying pre-CO recombination interactions and that stable autopolyploid meiosis can emerge by evolution of a “supercharged” interference process, which can now act effectively on such configurations. Thus, the basic interference mechanism responsible for simplifying CO patterns along chromosomes in diploid meiosis has evolved the capability to also simplify CO patterns among chromosomes in autopolyploids, thereby promoting bivalent formation. We further show that evolution of stable autotetraploidy preadapts meiosis to higher ploidy, which in turn has interesting mechanistic and evolutionary implications.