1. Combine 1 tablespoon juice, oregano, and 2 garlic cloves in a large zip-top bag. Add chicken to bag; seal. Let stand 10 minutes, turning once. Heat oil in a large skillet over medium-high heat. Remove chicken from bag; discard marinade. Sprinkle both sides of chicken evenly with salt and pepper. Add chicken to pan. Cook 5 minutes on each side or until done. Let stand 5 minutes; cut chicken crosswise into 1/4-inch-thick slices.
2. Combine remaining juice, remaining 1 garlic clove, mayonnaise, and next 3 ingredients (through tuna) in a food processor; process until smooth, scraping sides. Place 1 cup arugula on each of 4 plates. Arrange 1 chicken breast half on each plate; serve each serving with about 3 tablespoons sauce.