In a bowl, whisk together the marinade ingredients until well combined. Place the chicken in a shallow dish and coat it with 4 tablespoons of the marinade, ensuring even coverage. Set aside the remaining marinade to use as a dressing.
Heat 1 teaspoon of oil in a large grill pan or skillet over medium-high heat. Cook the chicken on both sides until golden brown and crispy. Use a meat thermometer to check that the internal temperature has reached at least 165°F before removing it from the heat. Let the chicken rest before slicing.
Slice the chicken into strips and assemble the salad with lettuce, avocado slices, tomatoes, mozzarella cheese, and the cooked chicken.
Sprinkle fresh basil on top, drizzle with the reserved dressing, and season with salt and pepper before serving.