Most patients with cancer either do not respond to immune checkpoint blockade or develop resistance to it, often because of acquired mutations that impair antigen presentation. Here we show that loss of function of the RNA-editing enzyme ADAR1 in tumour cells profoundly sensitizes tumours to immunotherapy and overcomes resistance to checkpoint blockade. In the absence of ADAR1, A-to-I editing of interferon-inducible RNA species is reduced, leading to double-stranded RNA ligand sensing by PKR and MDA5; this results in growth inhibition and tumour inflammation, respectively. Loss of ADAR1 overcomes resistance to PD-1 checkpoint blockade caused by inactivation of antigen presentation by tumour cells. Thus, effective anti-tumour immunity is constrained by inhibitory checkpoints such as ADAR1 that limit the sensing of innate ligands. The induction of sufficient inflammation in tumours that are sensitized to interferon can bypass the therapeutic requirement for CD8+ T cell recognition of cancer cells and may provide a general strategy to overcome immunotherapy resistance.