A raw breast has a lot of bones. Granted, it got chewed, but no better than it takes to get it swallowed. Stomach acid will soften it, but I'd be lying if I said how fast. And it may just soften it enough to get down into the gut. Possible problems aren't over until it is out of the dog.
Food allergies cause itching, not vomiting. The problem is a space occupying object that irritates the stomach. Anything that stimulates much stomach activity results in vomitting. If you have canned food, water it down into a gruel, or even thinner, and try this for nutrition.
No need to try to get it back up. It will come back on it's own if it can, but, like going south, it may get stuck coming 'north'.
Actually, we're speculating. There is only one way to confirm this... an x-ray. If confirmed, decision can be made whether to wait, or surgically remove it.
If there are no chicken parts there, consider something invisible to x-ray, and the advice of your vet.
As long as this has gone on, I think you may be able to wait till Monday before checking with your vet, but not longer.
Best wishes. Feel free if more questions.
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