Whisk together olive oil, lime juice, cilantro, garlic, brown sugar, chili flakes, cumin, and salt. Pour half into a dish and add the chicken, coating all sides well. Let it marinate for at least 30 minutes, and longer if you want richer flavor.
Heat a little oil in your grill pan over medium-high heat. Cook the chicken on both sides until golden and fully cooked. Let it rest a few minutes before slicing to lock in the juices.
Wipe the pan lightly and add a teaspoon of oil. Toss in the sliced peppers and onions. Cook until they soften and develop light char marks for that classic fajita flavor.
Slice the chicken into strips. Place the crisp lettuce in a bowl, then top with sautéed vegetables, avocado slices, and chicken. Drizzle the reserved marinade over the salad as your dressing. Add cilantro and optional sour cream before serving.