Layer the base ingredients: Place the chicken breasts in the bottom of the slow cooker. Add the white beans, kidney beans, diced tomatoes, chicken broth, celery, carrots, and onion on top.
Season the chili: Sprinkle garlic powder, smoked paprika, salt, and pepper over the top. Stir gently to distribute the seasoning through the liquid without disturbing the chicken too much.
Cook on low: Cover and cook on low for 6 hours, or on high for 3 to 4 hours, until the chicken is opaque throughout and pulls apart easily with a fork.
Remove and shred chicken: Lift the chicken breasts out onto a cutting board using tongs. Shred the meat into bite-sized pieces with two forks, checking that no pink remains.
Return chicken to pot: Add the shredded chicken back into the slow cooker, stirring it into the beans and broth so it's evenly distributed.
Stir in buffalo sauce: Pour in the buffalo sauce and stir well. The broth will start turning a deeper orange color as it mixes through the beans and vegetables.
Melt in cream cheese: Add the softened cream cheese and ranch dressing. Stir continuously for 2 to 3 minutes until the cream cheese fully melts and the broth looks creamy and uniform.
Let it rest: Turn off the slow cooker and let the chili sit uncovered for 5 to 10 minutes. It will thicken slightly as it cools a bit, reaching a spoonable consistency.
Taste and adjust: Taste the chili and add more buffalo sauce for extra heat or more ranch dressing to mellow it, adjusting salt and pepper as needed.
Serve with toppings: Ladle the chili into bowls and top with shredded cheddar cheese and sliced green onion. Set out extra ranch dressing on the side for anyone who wants more.
