Combine half the yogurt, half the lemon juice and zest, garlic, thyme, basil, olive oil, salt and pepper. Add in chicken breasts and allow to marinade for at least four hours.
Grill chicken for 6 minutes per side, until cooked to an internal temperature of 165 degrees F. Cover with foil and allow to rest.
While the chicken grills, bring the chicken stock to a boil. Add the Israeli couscous, cover and reduce heat to low. Cook for approximately 12 minutes, until most liquid is absorbed and the couscous is tender.
Add remaining Greek yogurt and goat cheese to the couscous. Turn off the heat and stir until the yogurt and cheese are well incorporated. Season with additional salt and pepper, to taste.
Transfer couscous to a large bowl or serving platter. Slice chicken breasts and place on top. Serve with extra wedges of lemon on the side.