My neighborhood has an HOA, I think most of the subdivisions here in Hutto do. I spoke to our animal control agent and she told me that it was fine to get chickens but to make sure to keep them out of neighbors yards, which is easy to do so no problem there. The bad news is that HOA covenants out rule city ordinances so even though it is legal to have backyard chickens in Hutto, your HOA may have a different view on that.
You can try to work around the issue by asking your neighbors "permission" before you get your chickens. Not that doing that will make your chickens "Legal" but it might help prevent your neighbors from turning you in to HOA. It's not going to be easy but I do believe that if you keep their coop clean and you follow all other HOA rules concerning your property, you won't draw as much attention to yourself and your birds. Good luck!