Trim any excess fat from the chicken and place the pieces in a mixing bowl.
Add 4 teaspoons olive oil and 1½ teaspoons balsamic vinegar to the bowl and toss the chicken with tongs to coat evenly.
Sprinkle the chili powder, paprika, cumin, garlic powder, dried oregano, onion powder, ½ teaspoon salt, and ½ teaspoon pepper over the chicken and toss again until well coated.
Arrange the chicken in a single layer in the air fryer basket (or in a hot skillet if not using an air fryer) and cook at 400°F in the air fryer for 10–12 minutes, or until the internal temperature reaches 160°F.
Remove the chicken to a cutting board and let rest 5 minutes, then thinly slice; squeeze lime over the sliced chicken if using.
While the chicken rests, heat 2 tablespoons olive oil in a large nonstick 12-inch pan over medium-high heat until hot.
Add the sliced bell peppers and onion in an even layer, season with ¼ teaspoon salt and ¼ teaspoon pepper, and cook, stirring only occasionally, until the vegetables are tender and charred in spots, about 10–12 minutes.
Divide prepared cilantro-lime rice or plain white rice among four bowls, top with sliced chicken and the pepper-onion mixture, then add desired toppings and serve immediately.