Mix wheat free tamari, lemon juice, and swerve together. Use most of it for marinade and about two tablespoons set aside for the dressing. Mix the part for the dressing with the mayo and swerve and put in the fridge.
Marinate the chicken in the non-dressing part for about an hour. Grill chicken to your liking.
Arrange mixed arugula and tomatoes on plate and top with the chicken and dressing.