The Tousled-like kinases 1 and 2 (TLK1/2) control histone deposition through the ASF1 histone chaperone and influence cell cycle progression and genome maintenance, yet the mechanisms underlying TLK-mediated genome stability remain uncertain. Here, we show that TLK loss results in severe chromatin decompaction and altered genome accessibility, particularly affecting heterochromatic regions. Failure to maintain heterochromatin increases spurious transcription of repetitive elements and induces features of alternative lengthening of telomeres (ALT). TLK depletion culminates in a cGAS-STING-TBK1-mediated innate immune response that is independent of replication-stress signaling and attenuated by the depletion of factors required to produce extra-telomeric DNA. Analysis of human cancers reveals that chromosomal instability correlates with high TLK2 and low STING levels in many cohorts. Based on these findings, we propose that high TLK levels contribute to immune evasion in chromosomally unstable and ALT+ cancers.