What are the requirements to run something like perchance ai chatlocally?

I have only a 1060 6gb, and not much ram but could maybe upgrade some more ram some day...anyway is it possible to run something like AI chat locally? It's made my life so much better and worth living (sad I know but it's truly awesome).

What would the requirements be, and what would it be like running it locally? Perchance's website is awesome but nothing is forever especially on the internet.