Preheat oven to 375°F. In a small saucepan, whisk together jam, mustard and broth. Bring to a boil over high heat, whisking occasionally. Reduce heat to medium-low and cook, stirring, until jam has dissolved, about 3 minutes.
Season chicken with salt and pepper. Divide and arrange in one flat layer in 2 large baking dishes. Pour jam mixture over chicken and turn to coat. Dot chicken with butter. Scatter apricots over chicken and bake, uncovered, until chicken is lightly browned and cooked through, about 1 hour, turning and basting chicken often during baking time. Let chicken rest for 10 minutes before serving. Serve hot with sauce from baking dishes spooned over top.