Mix together salt, pepper, chipotle, and cayenne. Coat chicken with the spice mixture.
Heat 2 tablespoons garlic infused olive oil in a large oven proof skillet over medium-high heat.
Add the carrots and saute for 5 minutes or until they begin to brown. Remove from pan and set aside.
Add 2 remaining tablespoons of oil to the pan over medium-high heat. Add seasoned chicken and cook for 4 minutes, then flip and cook for 4 more minutes.
Add the carrots to the chicken and zest the lime over the mixture.
Add lime juice, toss chicken and carrots to coat, and place the pan in the oven for ten minutes until chicken is cooked through.