Heat olive oil in Dutch oven over medium heat.
Add diced chicken and cook until golden brown.
Remove chicken and set aside in bowl.
Add onions to same pot and cook.
Sauté until soft and translucent, about 5 minutes.
Add minced garlic and cook 1 minute more.
Return chicken to pot with accumulated juices.
Add chopped apples, white beans, and chicken broth.
Stir in cumin, chili powder, salt, and pepper.
Bring mixture to a rolling boil over heat.
Reduce heat and let simmer 20 minutes.
Add shredded white cheddar cheese gradually while stirring.
Cook until cheese melts completely and chili thickens.