TL;DR
Yes, if it thawed in the refrigerator. Chicken thawed any other way should be cooked before it goes back in the freezer.
The panic move is dumping thawed chicken straight into the trash because it already thawed. That's usually unnecessary — the method of thawing is what decides whether refreezing is safe, not the fact that it thawed at all.
Refrigerator thawing keeps chicken at a safe, cold temperature the whole time, so bacteria never get a chance to multiply. Counter thawing or warm water thawing is a different story, because parts of the chicken can sit in the temperature danger zone.
How the chicken thawed changes everything
Chicken thawed in the refrigerator (at or below 40°F/4°C) stayed cold the entire time, so it's safe to refreeze raw within 1-2 days of thawing. Chicken thawed on the counter, in warm water, or in the microwave passed through the 40-140°F (4-60°C) danger zone, where bacteria multiply fast — that chicken should not go back in the freezer raw. If you're not sure how it thawed, check whether it still feels cold to the touch and whether the fridge it sat in was actually running at 40°F or below; a fridge thermometer settles the question faster than guessing.
Cook it first if you thawed it the fast way
If you used cold water thawing (chicken sealed in a bag, submerged, water changed every 30 minutes) or the microwave defrost setting, cook the chicken fully before freezing it again. Cook it to an internal temperature of 165°F (74°C), let it cool, portion it, and freeze it within about 2 hours of cooking. Cooked chicken freezes well and sidesteps the safety question entirely, since bacteria that could have built up during fast thawing gets killed in the process.
How long refrigerator-thawed chicken keeps
Raw chicken that thawed in the fridge is good for 1-2 more days in the fridge, or you can refreeze it during that window. Refreezing sooner rather than later protects both safety and texture — ice crystals from a second freeze pull moisture out of the meat, so expect it to be a little drier or chewier after cooking. Wrapping it tightly or vacuum sealing before the second freeze cuts down on freezer burn, which shows up as grayish-brown, dried-out patches on the surface.
When to just throw it out
Skip refreezing (and eating) if the chicken sat out above 40°F for more than 2 hours total (1 hour above 90°F/32°C), smells sour or sulfurous, feels sticky or slimy, or has a grayish or greenish tint. Those are signs bacteria have already built up, and refreezing won't undo that — freezing pauses bacterial growth, it doesn't reverse spoilage that already happened. When in doubt about how long chicken sat unrefrigerated, it's safer to discard it than to gamble on a meal.
The freezer isn't off-limits just because chicken thawed — it's off-limits if the chicken warmed up along the way. Thaw in the fridge next time and you'll have options either way.