Season chicken with 1/8-tsp salt and pepper. In a shallow Dutch oven, heat oil over medium-high heat and brown the chicken in batches. Transfer the chicken to a plate and set aside.
Reduce the heat to medium and saute the onion until golden. Add the leeks and the garlic, sauteing until the leeks are softened. Add the barley and bay leaf, stirring constantly for about 2 minutes. Then stir in the wine and cook until it evaporates. Add the chicken stock, mushrooms, thyme and remaining salt. Bring to a boil and reduce heat to low. Simmer for 10 minutes and then add the chicken, nestling it into the barley. Cover and cook until barley is tender and liquid is absorbed, about 1 hour for barley groats (35-40 minutes for pearl barley).