Final answer:
Chromosomes begin to condense and become visible under a microscope during Prophase of the cell cycle.
Step-by-step explanation:
The stage of the cell cycle in which chromosomes begin to condense and become visible under a microscope is Prophase. During Prophase, the loosely packed chromatin coils and condenses into visible chromosomes.
Each chromosome becomes visible with its identical partner attached, forming the familiar X-shape of sister chromatids. The nucleolus disappears early during this phase, and the nuclear envelope also disintegrates.