Cook the Chicken
Stovetop: Heat olive oil in a large pot or Dutch oven over medium-high heat. Season chicken breasts with salt and pepper. Sear for 5-7 minutes per side, until cooked through. Remove from pot and shred with two forks once cooled. Slow Cooker: Place chicken breasts in the slow cooker. Pour in 2 cups of chicken broth. Cook on low for 6-8 hours or high for 3-4 hours. Shred chicken when done. Instant Pot: Place chicken breasts in the Instant Pot. Pour in 1 cup of chicken broth. Cook on high pressure for 10 minutes, followed by a 10-minute natural pressure release. Shred chicken when done.
Sauté the Aromatics
In the same pot (or a clean pot if you used the slow cooker or Instant Pot for the chicken), heat olive oil over medium heat. Add chopped onion and cook until softened, about 5 minutes. Add minced garlic and cook for another minute until fragrant.
Build the Flavor Base
Add the remaining chicken broth, Great Northern beans, diced green chilies, cumin, oregano, chili powder, and smoked paprika to the pot. Season with salt and pepper to taste. Bring to a simmer and cook for 15-20 minutes, allowing the flavors to meld together.
Add the Chicken and Cream Cheese
Stir in the shredded chicken and softened cream cheese. Cook until the cream cheese is fully melted and incorporated, stirring frequently.
Taste and Adjust
Give the chili a final taste and adjust the seasoning as needed. Add more salt, pepper, or spices to your liking. If you prefer a spicier chili, add a pinch of cayenne pepper or a dash of hot sauce.