Add chicken and vegetables: Place the chicken breasts in the bottom of the crockpot, then add the onion, celery, and garlic around it.
Pour in liquids and beans: Add the diced tomatoes, chicken broth, white beans, and buffalo sauce over the chicken, stirring gently to combine everything.
Cook low and slow: Cover and cook on low for 6 hours or on high for 3 to 4 hours, until the chicken is cooked through and pulls apart easily with a fork.
Shred the chicken: Remove the chicken to a cutting board and shred it with two forks into bite-sized pieces.
Return chicken to pot: Add the shredded chicken back into the crockpot and stir it into the broth and beans.
Stir in cream cheese: Add the cubed cream cheese and ranch seasoning mix, stirring every few minutes until the cream cheese melts fully and the chili turns creamy and pale orange.
Adjust seasoning: Taste the chili and add more buffalo sauce for extra heat or a splash of broth if it's thicker than you like.
Let it rest: Turn off the crockpot and let the chili sit uncovered for 5 minutes to settle before serving.
Serve with toppings: Ladle the chili into bowls and top with shredded cheddar, a drizzle of ranch dressing, and sliced green onions.