Put the buffalo, chuck, onion, tomato paste, and liquid smoke in a large bowl and season generously with salt and pepper. Mix everything together with your hands until it is well combined.
Take about 1 cup (8 ounces) of the meat mixture and form it into patties with your hands or in a hamburger press. When you have them all made, grill them, turning frequently, until cooked through, about 8 to 10 minutes total. (Alternately, cook them in a large nonstick skillet over medium-high heat until cooked through, about 8 to 10 minutes.) Serve on hamburger rolls with the toppings of your choice.