Whisk vinegar, oil, Swerve, garlic, dried basil and salt together to combine. Place uncooked chicken in a shallow dish; pour a small amount of dressing over chicken and toss around to coat. Reserve unused dressing for later.
Heat grill or a small amount of oil in a pan over medium-high heat. Cook chicken until cooked through, set aside and allow to rest.
Slice chicken into strips and prepare salad with lettuce, tomatoes, mozzarella and chicken. Top with fresh basil. Drizzle with reserved dressing; season with salt and pepper if desired. Serve.