Place 1 can of the drained and rinsed beans in a food processor or blender. Add ¼ cup of the broth and puree until smooth; set aside.
Heat the oil in a large Dutch oven or stockpot over medium-high heat. Add onion and sauté until soft, about 7-10 minutes. Add garlic and green chilies; cook, stirring constantly, for 1 more minute.
Stir in the remaining chicken broth, pureed beans, remaining 2 cans of drained and rinsed beans, corn, cumin, paprika, oregano, thyme and cayenne. Season with salt and pepper, to taste. Bring to a boil over high heat. Once the chili boils, reduce heat to low and simmer, uncovered, stirring occasionally, for 30 minutes. If the chili gets too thick, cover with a lid while it continues to simmer.
After the chili has simmered for about 30 minutes, stir in the chicken and the cream cheese. Cook, stirring occasionally, for 5-10 more minutes (or until the cream cheese melts smoothly into the chili and the chicken is warmed through). Add a squeeze of lime juice just before serving and garnish individual bowls with desired toppings.