Heat the olive oil in a large Dutch oven or pot over medium-high heat. Brown the ground chuck until no longer pink. Add the celery, onions, bell peppers and garlic. Cook just until the vegetables start to soften, 3 to 5 minutes.
Add the tomato paste and stir to coat the vegetables. Next, add the crushed tomatoes, chili powder, cumin and cayenne. Bring to a boil, then reduce the heat and simmer, 45 minutes.
Add the beans to the liquid and simmer to heat through. Serve the chili topped with shredded Cheddar, chives and sour cream.