Heat olive oil in a large pot over medium-high heat.
Add chicken breasts. Cook 5 minutes per side until browned. Remove and set aside.
Add onion to the pot. Cook 4 minutes until soft.
Add garlic. Cook 30 seconds.
Pour in chicken broth. Scrape up browned bits from the bottom.
Add white beans, green chiles, cumin, chili powder, oregano, salt, and pepper.
Return chicken to the pot. Push it into the liquid.
Bring to a boil then reduce to medium-low.
Cover and simmer for 20 minutes.
Remove chicken. Shred with two forks.
Return shredded chicken to the pot.
Turn off heat. Stir in sour cream, cheese, and lime juice.
Taste and adjust seasoning.
Serve with cilantro, avocado, cheese, and tortilla chips.