Spread jam over cut side of top half of bread. Combine cheese and butter in a bowl, stirring until smooth. Spread cheese mixture over cut side of bottom half of bread. Arrange chicken evenly over cheese mixture; sprinkle with pepper. Place top half of bread, jam side down, over chicken.
Heat a large nonstick skillet over medium heat, and add sandwich to pan. Place a heavy cast-iron skillet on sandwich; cook 5 minutes or until both sides are browned, turning once.
Place arugula in a bowl. Drizzle juice over arugula; toss gently. Remove top bread half from sandwich. Arrange arugula mixture over chicken. Replace top bread half. Cut sandwich into 4 equal portions.