The organelle that organizes the motion of chromosomes during cell division is the centriole.

Here's how it works:

* Centrioles are small, cylindrical structures found in animal cells (and some plant cells).

* During cell division, centrioles replicate and migrate to opposite poles of the cell.

* They form the spindle fibers which are made of microtubules.

* The spindle fibers attach to the chromosomes at their kinetochores and pull them apart, ensuring that each daughter cell receives a complete set of chromosomes.

So, while the centriole itself doesn't directly move the chromosomes, it provides the structure and organization necessary for the spindle fibers to do their job.