In a medium pot, combine the chicken breasts, sweet chili sauce, soy sauce, and lime juice over medium heat. Cover and simmer for 15–20 minutes, stirring occasionally, until the chicken is fully cooked.
Shred the chicken into chunky pieces using two forks. Uncover the pot, reduce the heat to low, and let the Sweet Chili Chicken Wraps filling simmer until slightly thickened.
While the chicken cooks, wash and dry the lettuce and prepare all the vegetables.
To assemble, place lettuce on a tortilla, add shredded vegetables, and top with warm chicken (drain excess liquid).
Drizzle with extra sweet chili sauce, roll tightly, and serve immediately.