Final answer:
Crossing over, a key process in genetic recombination and variation, occurs between non-sister chromatids of a homologous pair of chromosomes during prophase I of meiosis.
Step-by-step explanation:
Crossing over occurs between two non-sister chromatids of a homologous pair of chromosomes. This is a crucial event during prophase I of meiosis where genetic material is exchanged between homologous chromosomes. This process also known as recombination, significantly contributes to the genetic diversity among organisms. It takes place when homologous chromosomes pair up gene-for-gene down their length forming a tetrad. The chromatids of these paired chromosomes, which are not sibling counterparts (non-sister chromatids), can then swap sections of their genetic material, leading to the creation of recombinant chromosomes, with a mix of maternal and paternal genes.