Season the chicken breasts in a bowl with salt, pepper, garlic powder, and ground ginger.
Mix sweet chili sauce and soy sauce in a separate bowl, pour half over the chicken, and marinate for at least 30 minutes in the refrigerator.
Heat olive oil in a large skillet over medium heat; cook the marinated chicken for 6-7 minutes on each side until fully cooked through.
Remove chicken from skillet, let rest for a few minutes, then slice into thin strips.
Warm tortillas in a microwave or skillet until pliable.
Assemble wraps by laying a tortilla flat, adding shredded lettuce, chicken slices, carrots, cucumbers, and cilantro, drizzling with remaining sweet chili sauce.
Fold in the sides of the tortilla and roll tightly.
Cut each wrap in half diagonally and serve immediately with lime wedges.
Notes
Marinate at least 30 minutes for better flavor. Serve warm for the best taste.