In prophase of mitosis, specialized regions on centromeres called kinetochores attach chromosomes to spindle fibers. The centromere is the part of a chromosome that links sister chromatids. During mitosis, spindle fibers attach to the centromere via the kinetochore. Kinetochores generate kinetochore fibers, which attach sister chromatids to spindle fibers. Kinetochore fibers and spindle polar fibers work together to manipulate and separate chromosomes during mitosis and meiosis.

The correct answer is option 'C': Kinetochore of the chromosome.

Explanation:
Spindle fibers, also known as microtubules, are responsible for separating the chromosomes during cell division. They attach to the chromosomes at a specialized region called the kinetochore. The kinetochore is a protein structure located at the centromere of the chromosome.

The centromere is the region of the chromosome where the sister chromatids are held together. It plays a crucial role in ensuring the proper alignment and separation of the chromosomes during cell division. The kinetochore is formed by proteins that are associated with the centromere region.

The spindle fibers extend from opposite poles of the cell and attach to the kinetochore of each chromosome. This attachment occurs through a complex interaction between the microtubules of the spindle fibers and the proteins of the kinetochore. Once attached, the spindle fibers exert forces on the chromosomes, pulling them towards the poles of the cell.

During mitosis, the spindle fibers are responsible for separating the sister chromatids, ensuring that each daughter cell receives the correct number of chromosomes. The proper attachment and alignment of the spindle fibers to the kinetochores are critical for the accurate segregation of the chromosomes.

In summary, spindle fibers attach to the kinetochore of the chromosome, which is located at the centromere region. This attachment is essential for the proper alignment and separation of the chromosomes during cell division.