The chromatin-remodeler ATRX is frequently lost in cancer cells that use ALT (alternative lengthening of telomeres) for telomere maintenance, but its function in telomere recombination is unknown. Here we show that loss of ATRX suppresses the timely resolution of sister telomere cohesion that normally occurs prior to mitosis. In the absence of ATRX, the histone variant macroH2A1.1 binds to the poly(ADP-ribose) polymerase tankyrase 1, preventing it from localizing to telomeres and resolving cohesion. The resulting persistent telomere cohesion promotes recombination between sister telomeres, while it suppresses inappropriate recombination between non-sisters. Forced resolution of sister telomere cohesion induces excessive recombination between non-homologs, genomic instability, and impaired cell growth, indicating the ATRX-macroH2A1.1-tankyrase axis as a potential therapeutic target in ALT tumors.