The present invention relates to methods for the in-situ treatment of ACM containing chrysotile asbestos using a polycarboxylic acid such as oxalic acid. The polycarboxylic acid is introduced to the ACM while it remains substantially in place, or "in-situ," and assists in converting the asbestos to a non-asbestos material. When the ACM is used as an insulating material, the asbestos fibers may be covered in gypsum that may be at least partially removed or dissolved away. The polycarboxylic acid may (1) directly attack the asbestos and/or (2) dissolve gypsum and form sulfuric acid capable of attacking the asbestos. Additional sulfuric acid may be introduced to assist in conversion of the asbestos to a non-asbestos form. Magnesium sulfate may be introduced to maintain the structural stability of the treated material thereby allowing it to substantially remain in place. Alternatively, the treated material may be safely removed for disposal.