Termination over Non-Complete Agreement

Can I be terminated from my job for refusal to sign an employment contract that included an unacceptable non-compete agreement, from a job that I was already doing? I am in NC an employment at will state.

Thanks

Yes, you can.

non complete termination

Thanks for your help. I had understood that a non-compete agreement can be required for employment but I thought it might be wrong to demand it as a condition of continuing employment. Thanks again