Chromosomal instability (CIN) drives cancer cell evolution, metastasis and therapy resistance, and is associated with poor prognosis. CIN leads to micronuclei that release DNA into the cytoplasm after rupture, which triggers activation of inflammatory signalling mediated by cGAS and STING. These two proteins are considered to be tumour suppressors as they promote apoptosis and immunosurveillance. However, cGAS and STING are rarely inactivated in cancer, and, although they have been implicated in metastasis, it is not known why loss-of-function mutations do not arise in primary tumours. Here we show that inactivation of cGAS-STING signalling selectively impairs the survival of triple-negative breast cancer cells that display CIN. CIN triggers IL-6-STAT3-mediated signalling, which depends on the cGAS-STING pathway and the non-canonical NF-κB pathway. Blockade of IL-6 signalling by tocilizumab, a clinically used drug that targets the IL-6 receptor (IL-6R), selectively impairs the growth of cultured triple-negative breast cancer cells that exhibit CIN. Moreover, outgrowth of chromosomally instable tumours is significantly delayed compared with tumours that do not display CIN. Notably, this targetable vulnerability is conserved across cancer types that express high levels of IL-6 and/or IL-6R in vitro and in vivo. Together, our work demonstrates pro-tumorigenic traits of cGAS-STING signalling and explains why the cGAS-STING pathway is rarely inactivated in primary tumours. Repurposing tocilizumab could be a strategy to treat cancers with CIN that overexpress IL-6R.