Chicken Chivito Sandwich

Preheat outdoor grill or large grill pan on high. From lemon, grate peel, and squeeze juice into food processor. Add olives, mayonnaise, vinegar, thyme, and pinch each salt and black pepper. Pulse until finely chopped; set aside. Brush chicken with 2 tablespoons oil and sprinkle with 1/4 teaspoon each salt and black pepper. Grill 5 to 7 minutes per side or until cooked through (165 degrees F). Transfer to cutting board. Brush cut sides of rolls with 1 tablespoon oil. Grill 1 to 2 minutes or until grill marks appear. In 12-inch nonstick skillet, heat remaining 2 tablespoons oil on medium. Add eggs; cook 1 minute. Turn eggs over; cook 1 to 2 minutes or until yolks are desired doneness. Sprinkle each egg with pinch of salt and black pepper. To assemble sandwich, spoon olive mixture onto bottom half of roll. Top with chicken, then ham, egg, arugula, and tomato. Replace top half of roll. Serve immediately.