Heat grill to medium-high. Once it is hot, clean the grill grate with a wire brush. Just before grilling, oil the grill grate.
Fill a large pot with 1 inch of water and fit with a steamer basket. Bring to a simmer. Place the potatoes in a steamer basket, and steam until tender, 15 to 18 minutes.
Whisk together the lemon juice, 2 tablespoons of the oil, ½ teaspoon salt, and ¼ teaspoon pepper in a large bowl. Add the arugula and potatoes and toss to coat.
Whisk together the marmalade, vinegar, the remaining tablespoon of oil, and 1/4 teaspoon each salt and pepper in a shallow dish. Add the chicken and turn to coat.
Grill the chicken until cooked through, 2 to 3 minutes per side. Serve with the salad.