As far as working with the original dealership for your warranty work it does help your case if you take it to the same dealership time after time and have a good working relationship with them as they may be more willing to fix things for you at no cost should you be out of warranty but do you strictly have to keep going to the same dealership should you get poor service at any point? No. You can go to a different dealership should you feel like you need to do so. Any GM dealership should be more than willing to do the warranty work for you as long as they have the tools and knowledge to do so as some brands (such as Saturn or SAAB) would require different knowledge sets for the mechanics that are working there. For Chevrolet specifically you should be able to go just about anywhere and get the service done. I hope that answers the questions you've got.

Jeff Morris, Chevrolet Customer Service