The dynamic regulation of microtubules during mitosis is critical for accurate chromosome segregation and genome stability. Cancer cell lines with hyperstabilized kinetochore microtubules have increased segregation errors and elevated chromosomal instability (CIN), but the genetic defects responsible remain largely unknown. The microtubule depolymerase MCAK can influence CIN through its impact on microtubule stability, but how its potent activity is controlled in cells remains unclear. Here we show that GTSE1, a protein found overexpressed in aneuploid cancer cell lines and tumours, regulates microtubule stability during mitosis by inhibiting MCAK microtubule depolymerase activity. Cells lacking GTSE1 have defects in chromosome alignment and spindle positioning due to microtubule instability caused by excess MCAK activity. Reducing GTSE1 levels in CIN cancer cell lines reduces chromosome missegregation defects, while artificially inducing GTSE1 levels in chromosomally stable cells elevates chromosome missegregation and CIN. Thus GTSE1 inhibition of MCAK activity regulates the balance of microtubule stability that determines the fidelity of chromosome alignment, segregation, and chromosomal stability.