In a large cast-iron skillet, melt the butter in the olive oil. Add the green pepper, onion, jalapeños, garlic, thyme and a generous pinch each of salt and pepper. Cook over moderate heat, stirring occasionally, until softened and just starting to brown, about 7 minutes. Stir in the potato and chicken and flatten the mixture with a spatula. Cook over high heat until crusty on the bottom, about 5 minutes. Working in sections, turn the hash over and cook until browned on the other side, 3 to 5 minutes.