Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the sliced chicken, fajita seasoning, salt, and black pepper. Cook for 5 to 6 minutes, stirring occasionally, until the chicken is browned and cooked through. Remove the chicken to a plate and set aside.
Add the remaining tablespoon of olive oil to the same skillet. Add the sliced peppers and onion. Cook for 6 to 7 minutes, stirring often, until the vegetables are softened but still have a little crunch.
Stir in the minced garlic and cook for 30 seconds until fragrant. Return the cooked chicken to the skillet and toss everything together for 1 minute to combine and warm through.
Warm the tortillas in a separate dry skillet or directly over a low flame for 20 to 30 seconds per side until soft and pliable.
Serve the chicken and vegetable mixture with the warm tortillas and lime wedges on the side.