Chromosomal instability, which is a characteristic of many human cancers, contributes to intratumour heterogeneity and has been functionally implicated in resistance to taxane therapy in tumour models. However, defining the status of tumour chromosomal instability in a given tumour to test this hypothesis remains challenging. Measurements of numerical and structural chromosomal heterogeneity demonstrate that histological grade correlates with chromosomal instability in oestrogen receptor (ER)-positive breast cancer. Using data on adjuvant taxane therapy in women with breast cancer, we propose that patients with low-grade ER-positive tumours, which are thought to be chromosomally stable, might derive unexpected benefit from taxane therapy. We discuss the implications of the relationships between tumour grade, chromosomal instability and intratumour heterogeneity, the development of high-throughput methods to define tumour chromosomal instability and the potential use of chromosomal instability to tailor therapy.