Heat the olive oil in a large Dutch oven over medium-high heat. Sear the bison in batches on all sides until golden brown. Add the carrots, celery and onion to the pot and cook until softened, about 5 minutes. Add the oregano, garlic, jalapenos and Hatch chile and cook until fragrant, about 1 minute. Add the tomato paste, chili powder and cumin and cook, stirring constantly, for 2 minutes. Add the tomatoes and 3 cups of water and bring to a simmer.
Cover the pot and simmer, stirring often, until the meat is tender, 2 to 3 hours. Add the beans in the last 20 minutes to heat through. Season to taste with salt and pepper. Serve with shredded Cheddar and Monterey Jack cheese.