Answer: It’s fine to refreeze the chicken breasts — as long as you thawed them in the refrigerator and kept them there for no more than two days. If that was the case, you can pop the chicken breasts back into the freezer and they’ll still be safe to eat, says the United States Department of Agriculture.ut keep in mind that thawing and refreezing any food will take a toll on its quality. In the case of your chicken breasts, you’ll likely see some changes in texture and taste after the second thaw.