You will be so lucky to move near Charleston! Absolutely gorgeous and fun!
Yes, there are many little towns near there where you can keep chickens. I bought some down on John's Island where she had goats and chickens. But there are many places that will allow them. The best thing to do is ask a Realtor when you know you have to move. They should be able to get you close to your job and find a area close that can allow chickens or small livestock. The commute is not too bad depending on where in Charleston you will have to go. My nephew lived in Summerville but worked in Charleston at one time. It didn't take him long to get to work unless there was an accident on the hwy, of course. But that happens in any town.