I don't have wide experience with different products, but the answer is yes. They're generally easy to setup and some are free. Generally, you're downloading a file, unzipping it, uploading to your server via FTP. You then run a setup program and set your parameters and preferences.
If you Google "forum software compared" it will give you an idea what's available, requirements, features and limitations, etc.
Thanks I found a few. I am still not sure I want to "own" this but I think our HOA could use a place to chat. We are starting to see a lot of younger folks moving in and if they can't do it on their phone, it doesn't exist.