Pat chicken breasts dry with paper towels. Place breasts between 2 sheets of heavy plastic on a solid, level surface. Firmly pound breasts with the smooth side of a meat mallet to a 1/2- to 3/4-inch thickness.

Combine cumin, chipotle chile powder, chili powder, smoked paprika, salt, coriander, garlic powder, Mexican oregano, and black pepper in a bowl; divide in half.

Sprinkle breasts with 1/2 spice mixture, rubbing on both sides. Transfer breasts to a plate; cover with plastic wrap and refrigerate for 1 hour to 8 hours.

Combine bell peppers, onion, and 1 tablespoon olive oil in a bowl; toss until vegetables coated with oil. Sprinkle reserved 1/2 spice mix over vegetables; toss until evenly coated. Set aside.

Heat a 12-inch cast-iron skillet over medium-high heat; add remaining 2 tablespoons oil. Add chicken breasts to the skillet; cook until nicely browned, 4 to 5 minutes per side. Transfer breasts to a cutting board.

Add vegetables to the same skillet; cook, stirring occasionally, about 5 minutes.

Meanwhile, slice breasts into 1/2-inch slices; return to the skillet. Cook and stir until chicken is no longer pink in centers and the juices run clear. An instant-read thermometer inserted into centers should read at least 165 degrees F (74 degrees C).

Off heat, drizzle lime juice over chicken fajitas; stir. Serve in warm tortillas.