DNA repair via homologous recombination (HR) is indispensable for genome integrity and cell survival but if unrestrained can result in undesired chromosomal rearrangements. The regulatory mechanisms of HR are not fully understood. Cyclic GMP‐AMP synthase (cGAS) is best known as a cytosolic innate immune sensor critical for the outcome of infections, inflammatory diseases, and cancer. Here, we report that cGAS is primarily a chromatin‐bound protein that inhibits DNA repair by HR, thereby accelerating genome destabilization, micronucleus generation, and cell death under conditions of genomic stress. This function is independent of the canonical STING‐dependent innate immune activation and is physiologically relevant for irradiation‐induced depletion of bone marrow cells in mice. Mechanistically, we demonstrate that inhibition of HR repair by cGAS is linked to its ability to self‐oligomerize, causing compaction of bound template dsDNA into a higher‐ordered state less amenable to strand invasion by RAD51‐coated ssDNA filaments. This previously unknown role of cGAS has implications for understanding its involvement in genome instability‐associated disorders including cancer.