1. Add 2 Tbsp. of the flour to a large bowl. Dry the chicken very well with paper towels. Add in the chicken cubes and toss to coat. Heat 1 Tbsp. of the olive oil in a dutch oven on medium-high heat. Add the chicken in batches, and sauté until well browned, about 6 to 7 minutes. Remove the chicken with a slotted spoon to a plate and set aside.
2. Add in another 1 Tbsp. of the oil. Add carrots, celery, and onions, and cook on medium heat until browned, about 8 to 10 minutes. Add the garlic and sauté for 1 minute, until fragrant. Add in the remaining flour and cook for 1 minute, until the flour coats the vegetables.
3. Add the wine, scraping up brown bits from the bottom of the pan. Bring to a boil, and reduce for 5 to 7 minutes while stirring. Add the chicken broth, tomato paste, thyme, and bay leaves. Add the chicken back to the pan. Bring to a boil, reduce heat to low, and simmer covered for 45 minutes.
4. While the chicken is simmering, in a large separate skillet, add the remaining 1/2 Tbsp. of olive oil, and sauté the pearl onions and mushrooms on medium-high heat until they are brown, about 6 to 8 minutes. Drain off any excess liquid. Set the pearl onions and mushrooms aside.
5. Remove the bay leaves from the pot and discard. Add the pearl onions and mushrooms to the chicken, and simmer uncovered for 5 to 7 minutes. Some of the liquid will evaporate, thickening the stew. Season with salt and pepper. Garnish with minced parsley.

Note: This stew may be served with additional vegetables and a salad, if desired.