Chromosomal rearrangements have a central role in the pathogenesis of human cancers and often result in the expression of therapeutically actionable gene fusions. A recently discovered example is a fusion between the genes echinoderm microtubule-associated protein like 4 (EML4) and anaplastic lymphoma kinase (ALK), generated by an inversion on the short arm of chromosome 2: inv(2)(p21p23). The EML4–ALK oncogene is detected in a subset of human non-small cell lung cancers (NSCLC) and is clinically relevant because it confers sensitivity to ALK inhibitors. Despite their importance, modelling such genetic events in mice has proven challenging and requires complex manipulation of the germ line. Here we describe an efficient method to induce specific chromosomal rearrangements in vivo using viral-mediated delivery of the CRISPR/Cas9 system to somatic cells of adult animals. We apply it to generate a mouse model of Eml4–Alk-driven lung cancer. The resulting tumours invariably harbour the Eml4–Alk inversion, express the Eml4–Alk fusion gene, display histopathological and molecular features typical of ALK+ human NSCLCs, and respond to treatment with ALK inhibitors. The general strategy described here substantially expands our ability to model human cancers in mice and potentially in other organisms.