Is it permissible to eat chicken from fast-food restaurants in America, and what is the ruling on eating chicken and meat at dinner invitations from Muslims when it is not known whether the animal was slaughtered according to Islamic law?

Allah has permitted good things for His servants and forbidden bad things for them, and this includes slaughtered animals. What is slaughtered according to Islamic law is permissible, and what is not slaughtered in the name of Allah or is slaughtered in an unlawful manner is forbidden. If chickens are slaughtered by Muslims or People of the Book in a lawful manner, then it is permissible to eat them; otherwise, it is not.