Pour olive oil into a large dutch oven or pot over medium heat. Add in the ground chicken and break it up with a wooden spoon while it cooks. When chicken is cooked through, remove it to separate plate or bowl and tent with aluminum foil to keep warm.
Add onions, carrots, and celery to the same pot you cooked the chicken in. Cook, while scraping the bottom of the pot to get the brown bits, for about 5 minutes. Add in garlic and hot peppers and cook for another 3 minutes. Sprinkle with salt and pepper.
Pour chicken stock into pot, along with the crushed tomatoes, black beans, and hot sauce. Let the mixture simmer for about 20 minutes. If your chili is too thick, add in a bit more chicken stock.
Serve in bowls and top with blue cheese.