In a small bowl, whisk together Greek yogurt, lemon juice, olive oil, herbs, salt and pepper. Pour into a gallon-size sealable bag and add chicken breasts. Squeeze all the air out of the bag and seal. Massage bag until chicken is well-coated in Greek yogurt mixture. Let chicken marinate in the refrigerator for at least one hour, ideally 3 hours.
Heat oven to 375°F.
In a 9x13-inch baking dish, add broth, rice, sweet potato, onion, garlic, herbs, salt and pepper. Whisk to mix. Place dish in the oven and bake for 20 minutes.
Remove from oven, and add chicken atop the dish. Scoop any remaining Greek yogurt mixture out of the bag and spread on chicken. Top chicken breasts with shredded Emmentaler cheese.
Return baking dish to the oven, and bake an additional 30 minutes or until rice has absorbed nearly all the liquid and chicken is cooked through.
Switch oven to broil set on high. Brown the chicken and rice until bubbling and golden. Remove dish from the oven, and let sit for 5 to 10 minutes. Rice will continue to cook through. Garnish with additional fresh herbs, if desired. Serve immediately and enjoy!