Dice onion and bell peppers into even 1/4-inch pieces, mince garlic, drain and rinse beans, open cans of tomatoes and chiles, measure spices, and soften cream cheese if using.
Heat olive oil in a Dutch oven over medium-high heat. Season chicken with salt and pepper, then sear for 3-4 minutes per side until golden brown. Remove chicken and set aside.
Reduce heat to medium. Add onion and bell peppers to the pot and cook for 5-6 minutes until softened and translucent. Add minced garlic and cook for 1 minute, stirring constantly.
Add chili powder, cumin, smoked paprika, garlic powder, onion powder, cayenne, salt, and pepper to the pot. Toast spices for about 60 seconds, stirring constantly to activate their oils.
Pour in fire-roasted tomatoes with their juices, tomato sauce, diced green chiles with their liquid, and chicken broth. Stir to combine everything into a unified base.
Add drained and rinsed kidney beans and black beans, stirring gently to distribute. Return seared chicken to the pot, nestling it into the liquid so it is mostly submerged.
Bring chili to a boil, then reduce heat to a low simmer. Cover with the lid slightly ajar and simmer for 20-25 minutes until chicken is fully cooked through (165°F / 74°C).
Remove chicken to a cutting board, let cool slightly, then shred with two forks into medium-sized pieces. Return shredded chicken to the pot and stir to incorporate.
For creamy chili, add softened cream cheese cut into cubes and stir over low heat until fully melted and smooth, about 2-3 minutes.
Squeeze lime juice over the chili and stir it in. Taste and adjust seasoning with more salt, cayenne, or lime as desired. Serve hot with your favorite toppings.