In a skillet, heat 1 tablespoon of the oil. Add the leeks and cook over moderate heat, stirring, until softened, about 7 minutes.
Add the mushrooms and season with salt and pepper. Cover and cook, stirring, until the mushrooms are tender, about 4 minutes. Scrape the leeks and mushrooms onto a plate.
Season the chicken with salt and pepper and lightly dust with flour, shaking off any excess.
Heat the remaining 1 tablespoon of oil in the skillet. Add the chicken and cook over moderate heat until golden brown, about 2 minutes per side.
Add the chicken stock and thyme and simmer over moderate heat until the chicken is just cooked through, about 1 minute.
Using a slotted spoon, transfer the chicken to the plate with the vegetables.
Simmer the stock over moderately high heat until reduced by half, about 2 minutes.
Return the chicken, leeks, and mushrooms to the skillet and simmer over low heat until warmed through, about 1 minute.
In a small bowl, blend the sour cream with the mustard and stir into the stew.
Remove the skillet from the heat. Season the stew with salt and pepper and serve.
