I had a coworker a couple years ago who brought in his own chair (a Herman Miller Aeron). When we came in after a weekend it had been removed and replaced with a cheap, office special that was the default in the cubicles. After a couple days he found it. The facilities manager had moved it into a VPs office because it was an “executive” chair. He had to go through a couple levels of approval, a meeting, and get the chair tagged in order to keep it. Dystopian.

I was having pretty significant back pain when I worked for a very small company and decided to buy a chair with fancy adjustable lumbar support. It's 15 years later and I have brought my own chair to every office I've ever worked in.

Your employer should provide an adequate chair. Even the US federal government is capable of meeting that bar, albeit with more delays and paperwork than a private-sector employer.