The crossing over takes place during the pachytene stage of prophase I of meiosis.

Explanation:
Prophase I is the first stage of meiosis I, which is further divided into five substages: leptotene, zygotene, pachytene, diplotene, and diakinesis. During the prophase I, homologous chromosomes pair up and exchange genetic material through a process known as crossing over. This results in the formation of recombinant chromosomes that carry a combination of genetic material from both parents.

The crossing over occurs during the pachytene stage, which is characterized by the following events:

1. Homologous chromosomes pair up: The homologous chromosomes come together and form a bivalent or a tetrad.

2. Synapsis: The paired homologous chromosomes undergo synapsis, which is the physical association of the homologs.

3. Crossing over: The chromatids of the homologous chromosomes exchange genetic material at specific sites known as chiasmata. This leads to the formation of recombinant chromosomes.

4. Formation of the synaptonemal complex: The synaptonemal complex holds the homologous chromosomes together and facilitates the exchange of genetic material.

5. Nuclear envelope breakdown: The nuclear envelope breaks down, and the spindle fibers attach to the chromosomes.

In conclusion, the crossing over takes place during the pachytene stage of prophase I of meiosis.

Pachytene. During the third substage of meiosis, the chromosomes continue to condense. Crossing over takes place at this stage and at each point of crossing over a chiasma is formed (singular: chiasma) between non-sister chromatids of homologous chromosomes.