Just like antique cars are hard to find even the car parts for any antique car are harder to find and even the classic Chevy car parts. People who have a hobby of collecting cars also collect the antique car parts. Some may choose to sell them but the price will be very high for such car parts.
There are different things that cars might need right from car upholstery, headlights, engine overhaul kits, shock absorbers and so on. Whatever a classic car like the Chevy needs will be available with these people. There are some companies not the famous ones but some small companies which do make car parts for the classic Chevy. With the help of internet you can search for people who sell the classic Chevy car parts. You will be surprised to find quite a few who sell the car parts for a classic Chevy.
There are lots of links listed in the classic car category which take you to the websites which has information listed about the classic chevy car parts or any auto car parts. These websites give you information about what car parts are available and where to find them. They also give the phone number listed and also have facilities to ship the car parts to you if you order with them. Some critical parts are hard to find but the chances that your precious antique car would need them are also slim. Because the major parts are not usually in demand they do not make them all that much. But otherwise car accessories for your classic Chevy must be easy to find.