In a small bowl, combine ground cumin, chili powder, smoked paprika, dried oregano, cayenne pepper, salt, and black pepper. Set aside.
Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat.
Add the thinly sliced chicken breast to the skillet and sprinkle half of the spice mixture over the chicken. Stir-fry for 5-6 minutes until the chicken is cooked through and slightly browned. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil.
Add the sliced red, yellow, and green bell peppers, and sliced onion to the skillet. Stir-fry for 4-5 minutes until the vegetables are tender-crisp.
Add the minced garlic and the remaining spice mixture to the vegetables. Stir-fry for 1 minute until fragrant.
Return the cooked chicken to the skillet with the vegetables. Stir well to combine and heat through for 2 minutes.
Remove the skillet from heat and stir in the fresh lime juice and chopped cilantro.
Serve the Mexican Chicken Stir-Fry hot over cooked rice, quinoa, or warm tortillas.