Season the chicken, peppers, and onion with salt and pepper and place on the hot grill. Allow the first side of the chicken to cook for about 6-8 minutes untouched (don't press down or move the chicken.) Add peppers and onions to the grill. Flip the chicken to the other side and allow it to cook untouched about 6-7 minutes more.
Meanwhile, squeeze all of the juice from half of a lemon into a small mixing bowl. Add the olive oil, oregano, garlic powder, and feta, and season with salt and pepper. Whisk until all ingredients are well combined, and set aside.
When the chicken is just cooked through, remove it from the grill and allow it to rest about 5 minutes, covered. Also remove the peppers and onions. Brush the lemon-herb dressing all over the grilled chicken and veggies. Serve over rice, quinoa, farro, or couscous.