Heat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Warm olive oil in a large skillet over medium heat.
Sauté onion and bell pepper until tender, 5 to 6 minutes.
Stir in garlic and cook until fragrant, about 30 seconds. Remove from heat.
In a big bowl, mix chicken, rice, black beans, corn, and tomatoes.
Whisk broth, sour cream, chili powder, cumin, smoked paprika, oregano, salt, pepper, and lime juice.
Pour the sauce over the chicken mixture. Fold in cilantro and half the cheese.
Add the sautéed vegetables. Stir until evenly combined.
Spread mixture in the baking dish. Top with remaining cheese.
Cover with foil and bake 20 minutes, until hot and bubbling at edges.
Uncover, sprinkle with crushed tortilla chips, and bake 10 to 15 minutes more.
Rest 10 minutes. Garnish with green onions and extra cilantro. Serve warm.