Pat chicken breasts dry with paper towels and slice against the grain into thin 1/4-inch (6mm) strips.
In a medium bowl, whisk together lime juice, lime zest, minced garlic, 2 tablespoons olive oil, cumin, smoked paprika, oregano, chili powder, salt, and pepper until fully combined.
Place chicken strips in a zip-lock bag or shallow dish, pour marinade over, and coat thoroughly. Refrigerate for at least 30 minutes or up to 4 hours.
Slice bell peppers and onion into thin 1/4-inch (6mm) strips, removing seeds and membranes from peppers.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add peppers and onion with salt and pepper, cooking 5-7 minutes until slightly softened and caramelized. Remove and set aside.
Increase heat to high. Remove chicken from marinade, letting excess drip off. Add to skillet in a single layer and cook 3-4 minutes per side until golden and cooked through (165°F/74°C). Let rest 2 minutes.
Wrap tortillas in a damp paper towel and microwave 30-45 seconds, or wrap in foil and warm in a 275°F (135°C) oven for 10 minutes.
Return vegetables to skillet with chicken and toss over medium heat for 1 minute to combine. Serve on warm tortillas with desired toppings.