In a bowl, whisk together soy sauce through sesame oil. Reserve 1⁄4 cup of marinade.
Add remaining marinade and chicken breasts to a ziploc bag or large bowl. Marinate in the fridge for at least 30 minutes. Remove chicken from bag/bowl and discard the marinade.
Heat grill to medium heat. Add chicken and cook for 57 minutes on each side, basting with reserved marinade while cooking.