Bring chicken broth and 1/2 teaspoon salt to a boil in a saucepan. Stir in couscous. Remove from heat; cover and let stand until broth is absorbed, about 5 minutes. Uncover and fluff with a fork.
Whisk 1/2 teaspoon salt, 1/2 cup olive oil, lemon juice, rosemary, and oregano together in a bowl to make dressing.
Place chicken breasts in a shallow dish. Drizzle 1/4 cup dressing on top. Season both sides with salt and pepper.
Heat 1 tablespoon olive oil in a large skillet over medium-high heat. Add chicken breasts; cook until golden brown, about 3 minutes per side. Transfer to a large plate. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Place 3 tablespoons dressing in a large bowl; stir in sugar. Add tomatoes, cucumber, and red onion; toss to combine. Season with salt and pepper. Add feta cheese and toss again.
Drizzle remaining dressing over couscous and fold in olives. Divide couscous among 4 plates. Slice chicken breasts and place on top. Serve tomato salad on the side. Sprinkle parsley over each plate.