During late prophase 1 of meiosis, chromosomes are....

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Crossing-over of the chromosomes to exchange genetic material occurs during the Prophase 1 phase of Meiosis. To be specific, there are 2 major additional steps to Prophase 1 of Meiosis compared to Prophase of Mitosis and these are:

Zygotene (Synapsis) - This is the pairing of the two homologous chromosomes.

Pachytene (Crossing-Over) - This is where the homologous chromosomes "cross-over" to exchange their genetic material.

Now, the synthesis of DNA does not occur in Cell Division but rather at a different part of the Cell Cycle. This is called the Interphase. Interphase is divided into three parts: S-phase, G1 and G2 Phase. The S-Phase stands for Synthesis Phase and this is where the chromosomes synthesize.

During late prophase 1 of meiosis 1 chromosomes are already condensed, homologous chromosomes synapse and crossing over takes place.