They'll be going on the grill.
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So long as you are planning to then cook your vegetables to 165ºF, I don't think there would be any food-safety issues with that.
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I wouldn't suggest it. As PhillipBrandon says, they'll need to be cooked to the same temperature as the chicken. At that point, I think they may be overcooked. Marinade them and handle them separately, and you'll have no worries.
Same thing as making a soup or whatever. Except I know soup will get up to 210F, will the interior of the vegetables get to 165?
It's sweet, salty, and just a little bit tangy.
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