Chromosomal instability is a hallmark of human cancer that is associated with aggressive disease characteristics. Chromosome mis-segregations help fuel natural selection, but they risk provoking a cGAS-STING immune response through the accumulation of cytosolic DNA. The mechanisms of how tumors benefit from chromosomal instability while mitigating associated risks, such as enhanced immune surveillance, are poorly understood. Here, we identify cGAS-STING-dependent upregulation of the nuclease TREX1 as an adaptive, negative feedback mechanism that promotes immune evasion through digestion of cytosolic DNA. TREX1 loss diminishes tumor growth, prolongs survival of host animals, increases tumor immune infiltration, and potentiates response to immune checkpoint blockade selectively in tumors capable of mounting a type I interferon response downstream of STING. Together, these data demonstrate that TREX1 induction shields chromosomally unstable tumors from immune surveillance by dampening type I interferon production and suggest that TREX1 inhibitors might be used to selectively target tumors that have retained the inherent ability to mount an interferon response downstream of STING.