Depends what you mean by without AOC. If you just mean whether Banach-Tarski can be proven in ZF the answer is no. But you also don't need the full power of AOC

Depends what you mean by without AOC. If you just mean whether Banach-Tarski can be proven in ZF the answer is no. But you also don't need the full power of AOC to prove Banach-Tarski.