Heat the olive oil in a large skillet over medium heat. Add the onion and thyme; season with salt and pepper. Cook, stirring occasionally, until golden brown, 8 to 10 minutes; let cool.
Roll and stretch the dough into a 12-inch square on a lightly floured surface. Spread the creme fraeche over the dough. Top with the onion mixture and the ham and chives. Cut the dough into 16 small squares and make 4 stacks of 4 squares each.
Place each stack on its side in a buttered 9-by-5-inch loaf pan. Gently separate the dough layers so the dough fills the pan.
Cover the loaf loosely with plastic wrap and set aside in a warm place until the dough rises by half its size, 1 to 2 hours.
Preheat the oven to 350. Bake the loaf until it's browned and cooked through, 40 to 45 minutes (tent with foil if it's browning too quickly). Let cool 15 minutes in the pan, then loosen the edges with a knife. Remove to a plate and let cool 30 minutes.