How bad can a liver be damaged from a chronic overdose on aspirin?

Not at all: Aspirin (asa or acetylsalicylic acid) is not toxic to the liver (but Acetaminophen or tylenol (acetaminophen) is if taken in large doses). Asa overdose is also dangerous, but has very different toxic effects - it notoriously causes ringing in the ears, damages the lining of the stomach, and leads to complex metabolic problems, which can be fatal.