Heat 1 tablespoon olive oil in a large pot or Dutch oven over medium-high heat. Season chicken pieces with salt and pepper, then add to the pot in a single layer. Cook until browned on all sides, about 4–5 minutes. Remove chicken to a plate.
Reduce heat to medium. Add the remaining 1 tablespoon oil, onion, and bell pepper. Cook, stirring occasionally, until softened, about 5 minutes. Stir in garlic, chili powder, cumin, smoked paprika, oregano, and cayenne (if using). Cook for 1 minute until fragrant.
Pour in the fire-roasted tomatoes with their juices, kidney beans, black beans, corn, and chicken broth. Stir to combine, scraping up any browned bits from the bottom of the pot.
Return the seared chicken (and any accumulated juices) to the pot. Bring the chili to a boil, then reduce the heat to low and simmer, partially covered, for 20–25 minutes, until the chicken reaches an internal temperature of 165°F (74°C) and the flavors have melded.
Taste and adjust seasoning with salt and pepper. Ladle into bowls and add your favorite toppings. Serve with lime wedges and tortilla chips.