There are different antonyms for the word "chaseable" depending on the context. In the sense of being able to pursue or catch, some antonyms are elusive, unattainable, and uncatchable. On the other hand, if "chaseable" implies something undesirable, for instance, a threat or an obstacle, suitable antonyms would be avoidable, unthreatening, or harmless. In a similar vein, if "chaseable" refers to an idea, a question, or a mystery, antonyms could be transparent, straightforward, or readily understandable. In sum, antonyms for "chaseable" vary based on the context they are used in, and they can signal different nuances of meaning.