I use a 5 gallon bucket with swivel top. 100% noise free.
If you need a swivel "chair" per se with backrest, I've been told by a number of hunters avoid the Cabela's brand 360 degree swivel chair. It tends to become squeaky in cold weather.
I've got a dove field bucket with roller swiver type seat on it. Tad noisy.
What brand do you have/like?