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Joy I don't cook chicken very often , if I have to cook it I would make sure it has thawed fully first otherwise the outside could be done while the inside is still raw.
To help thaw a piece of chicken quickly you can put it in a plastic bag then place it in a basin of cold water ...
No, I wouldn't cook it, until it is fully thawed.
Would it help if you could quarter it? I believe it is 2 hours per 4lb for the cold water method that Meg suggested.