Final answer:
The thylakoid membranes of the chloroplast contain photosynthetic pigments like chlorophyll, which are essential for absorbing light during photosynthesis.
Step-by-step explanation:
The part of the chloroplast that has photosynthetic pigments in its membrane is the thylakoid. Photosynthetic pigments such as chlorophyll are embedded in the thylakoid membrane. These pigments are vital for the process of photosynthesis as they absorb light energy. The thylakoid membranes form stacks called grana, and the space outside these membranes is known as the stroma, where the light-independent reactions of photosynthesis, often called the Calvin cycle, take place.