Heat oven to 400º F. In a small bowl, mix the marmalade and chili-garlic sauce.
Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper.
Roast on a foil-lined baking sheet until cooked through, 30 to 35 minutes, brushing with the marmalade mixture during the last 10 minutes of cooking.
Meanwhile, bring a pot of salted water to a boil. Cook the green beans until tender, 4 to 6 minutes.
Drain and toss with the butter and 1⁄4 teaspoon each salt and pepper. Serve with the chicken and muffins.