2. Heat 1 tablespoon of the oil in a wide, shallow pot over medium heat. Add the chicken and brown on all sides, about 2 minutes on each side. The oil should be hot enough to sear in the juices but not burn. Remove the chicken from the pan and drain off the excess fat.
3. Turn the heat to medium-high and add the vegetables. Cook for 3 to 4 minutes, until they begin to soften. Turn up the heat and brown slightly. (This can be made ahead and kept in the refrigerator up to 3 days or frozen.)
4. Add the bay leaf, thyme and red wine, and cook until the wine is almost completely evaporated.
5. Put the seared chicken back in the pot and cover with stock. Bring to a simmer and cook, uncovered, for 1 1/2 hours. Do not let it boil rapidly.
6. Strain the stew and retain the chicken and liquid. Discard the vegetables. Return the liquid to the pot and simmer to reduce its volume by half.
7. Meanwhile, bring a small pot of salted water to a boil. Add the pearl onions and cook until tender, about 5 to 7 minutes. Drain and set aside.
8. Heat the remaining tablespoon of oil in a small skillet over medium-high heat. Add the mushrooms, season them with salt and pepper and cook for 4 to 5 minutes. Remove from heat.
9. Remove the skin from the chicken; discard the skin. Add the chicken, mushrooms and onions to the reduced liquid.
10. Adjust the seasoning with a generous amount of salt and pepper.