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Is old celery really toxic? I have one in my fridge. I was going to eat at least the few crisp-ish stalks in the center, but now I think I will just throw the whole thing out.

If there are a few crisp-ish stalks, look and see if they are turning white or brown... if they are still green, they are, at least according to my research, still all right. But if they are getting limp and turning colors, let 'em go to the compost bin. Old celery can cause food poisoning long before you get enough to cause cancer... but Thalia went for the biggest gusto she could to get that owner to do what he needed to do.