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Marinate the Chicken: In a bowl, combine the sliced chicken with chili powder, ground cumin, paprika, garlic powder, salt, pepper, and lime juice. Let it marinate for at least 30 minutes in the refrigerator.
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Prepare the Filling: Heat olive oil in a large skillet over medium-high heat. Add sliced bell peppers and onions. Sauté until they start to soften, about 5-7 minutes. Add minced garlic and cook for another minute. Remove the vegetables from the skillet and set aside.
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Cook the Chicken: In the same skillet, add the marinated chicken strips. Cook until they are browned and cooked through, about 6-8 minutes. Remove from the skillet and set aside.
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Assemble the Burritos: Lay out the flour tortillas on a clean surface. Spoon a quarter of the cooked rice onto each tortilla, followed by a quarter of the cooked chicken, sautéed vegetables, black beans, shredded cheese, and salsa.
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Fold the Burritos: To fold each burrito, fold the sides of the tortilla over the filling, then roll it up tightly from the bottom, tucking in the sides as you go.
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Serve: Optionally, you can warm up the burritos on a skillet or in the microwave before serving. Serve the chicken fajita burritos with sour cream, guacamole, chopped cilantro, and lime wedges on the side.