Heat 1 tablespoon of olive oil in a large skillet or wok over medium-high heat.
Add the chicken strips to the skillet, season with salt and black pepper, and cook for 5-6 minutes until the chicken is cooked through and lightly 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 onions and bell peppers to the skillet and sauté for 4-5 minutes until they begin to soften but still retain some crunch.
Add the minced garlic and cook for an additional 30 seconds until fragrant.
Return the cooked chicken to the skillet with the vegetables.
Sprinkle the ground cumin, chili powder, smoked paprika, dried oregano, cayenne pepper, salt, and black pepper over the chicken and vegetables.
Stir well to evenly coat everything with the spices and cook for another 2-3 minutes to allow the flavors to meld.
Remove the skillet from heat and stir in the chopped cilantro and fresh lime juice.
Serve the Mexican Chicken Stir-Fry hot with your choice of rice, tortillas, or as is.