Approximately 10% of tumors including all IDH1-mutant lower-grade glioma resolve telomeric shortening using Alternative Lengthening of Telomere (ALT) mechanism. Although the ALT process lengthens telomeres, it also generates small bits of extrachromosomal, telomere-containing DNA (ECTRs). These ECTRs can bind and activate cyclic GMP-AMP synthase (cGAS), the major cytosolic sensor of double-stranded DNA, which in turn can activate expression of stimulator of IFN genes (STING) and the interferon-based innate immune response. To limit the immune response, ALT cells inactivate the cGAS-STING pathway, although the mechanism by which this occurs is unknown. Here we show that the deubiquitinase BRCC3 links ALT telomeres to suppression of the cGAS-STING pathway and the innate immune response. Astrocytoma cells dependent on the ALT-mechanism (IDH1-mutant and ATRX-deficient genetically-modified human astrocytes and MGG119 PDX) contained ECTR and had reduced expression of the cGAS and the downstream components of the cGAS-STING pathway (STING, and IFN-β) relative to matched non-ALT (isogenic ATRX WT astrocytes and MGG152 PDX) cells lacking ECTRs. Decreased levels of cGAS in ALT cells were in turn associated with deubiquitiantion and destabilization of cGAS. The telomere-derived ECTR in ALT-dependent cells lacked two proteins normally found in ALT telomeres (TRF2 or PARP), but retained two other proteins, Mre11 and its binding partner, normally nuclear deubiquitinase BRCC3. Furthermore, either pharmacologic inhibition or genetic suppression of BRCC3 levels had no effect on ECTR levels but stabilized cGAS and activated the cGAS-STING pathway. This cGAS-mediated activation could be blocked by exogenous expression of WT BRCC3, but not by expression of a mutant BRCC3 incapable of deubiquitination. These results show that BRCC3 translocated along with ECTRs to the cytoplasm degrades cGAS and protects ALT-dependent cells from activating the innate immune response. The BRCC3-controlled cGAS-STING pathway may therefore represent a therapeutically targetable means to enhance the immune response in IDH1-mutant lower grade glioma.