Whisk together marinade ingredients to combine. Place chicken in a shallow dish; pour 4 tablespoons of the dressing/marinade onto the chicken and stir to coat evenly. Reserve the remaining marinade for dressing later.
In a large grill pan or skillet, heat about one teaspoon of oil over medium-high heat and grill or sear the chicken fillets on each side until golden, crispy, and cooked through. Once the chicken is cooked, set aside to rest.
Slice the chicken into strips, then prepare the salad with lettuce, avocado slices, tomatoes, mozzarella cheese, and chicken. Top with basil strips, drizzle with remaining dressing, season with salt and pepper, and serve.