Heat a large heavy-bottomed skillet over high heat. Add the butter, olive oil and maple syrup, stir well. As soon as the butter is melted, add the Brussels sprouts and chestnuts and toss carefully with two wooden spoons (so as not to break the chestnuts) until the ingredients are well coated with the oil. Sauté for 7 to 8 minutes until golden-brown, tossing only occasionally. Reduce heat to medium-high, add the shallots, salt and pepper and sauté for 1 to 2 minutes until shallots have softened. Transfer to a serving platter and serve immediately.