The cellular structure which traces the movement of chromosomes during mitosis is the centrioles. Centrioles are mainly constructed of microtubules and are responsible for directing the movement of chromosomes during mitosis.
Mitosis is the process of the cell cycle where one cell splits its duplicated genetic material into two identical cells. Centrioles are part of the mitotic spindle which is the structure that organizes and moves the chromosomes into these two daughter cells.