Heat the olive oil in a large Dutch oven over medium heat. Add the chicken pieces and cook until lightly browned on all sides.
Stir in the onion, carrots, and celery. Cook for 5 minutes until the vegetables begin to soften.
Pour in the chicken broth and add the thyme, salt, and pepper. Bring the mixture to a simmer and let it cook for 15 minutes.
While the broth simmers, stir together the flour, baking powder, and milk in a bowl to form a thick dumpling batter.
Drop spoonfuls of the batter directly into the simmering broth. Cover the pot and cook for 12 minutes without lifting the lid so the dumplings steam through.
Remove the pot from the heat and sprinkle the chopped parsley over the top before serving.