Heat oven to 350°F. Grease 15 x 10 x 1-inch jelly-roll pan.
Wrap tortillas in damp paper towels; microwave until warm and flexible, about 1 minute. Or, wrap tortillas in foil; heat in 350°F oven for 10 minutes.
Spread 1 tortilla on work surface; keep remaining tortillas warm. Top tortilla with 3/4 cup chicken chili. Sprinkle with 1/4 cup cheddar cheese. Wrap up tortilla, envelope fashion, to enclose filling. Transfer burrito, seam side down, to prepared jelly-roll pan. Repeat with the remaining tortillas, chili and cheddar cheese.
Bake in 350°F oven until tortillas are crispy, filling is heated through and cheese is melted, about 30 minutes. Let burritos cool slightly. Serve with sour cream and salsa on the side.