Place processed cheese into a slow cooker and set to Low. Stir occasionally until melted.
Meanwhile, cook sausage in a large skillet over medium-high heat until evenly browned. Stir frequently and break into small crumbles. Drain the grease, and stir into the cheese in the slow cooker. Mix in the cheese soup and green chilies. Keep warm in the slow cooker, and serve with tortilla chips.