Which structure is known to facilitate the movement of chromosomes within a cell?

The structure that is known to facilitate the movement of chromosomes within a cell is the spindle fibre. Spindle fibres are crucial components of the spindle apparatus, which forms during cell division, specifically during mitosis and meiosis. These fibres are made of microtubules and are responsible for attaching to the chromosomes at their centromeres, helping to align them along the metaphase plate and subsequently pulling them apart to ensure that each daughter cell receives an identical set of chromosomes.

The spindle fibres originate from the centrosomes, which serve as the main microtubule organizing centers in animal cells. However, while the centrosome is important for organizing the spindle fibres, it does not directly facilitate the movement of the chromosomes itself.

In contrast, genes and alleles are related to heredity and the storage of genetic information but do not play a role in the physical movement of chromosomes during cell division. Thus, the spindle fibre is specifically designed for managing the dynamics of chromosome segregation, making it the correct answer to the question.