1. Arrange the chicken breasts in a singly layer on a work surface and cover with plastic wrap. Using a heavy skillet or a rolling pin, pound them until flattened to about 1/2 inch thick.
2. In a shallow dish, combine the flour, 1 teaspoon of salt and 1/2 teaspoon of pepper. Dredge both sides of each breast through the seasoned flour to lightly coat.
3. In a large nonstick skillet over medium-high, heat the oil and butter. Add the chicken breasts and cook until they are well browned on both sides, about 4 minutes per side. Transfer them to a plate and cover with foil to keep warm.
4. Add the mushrooms and leeks to the skillet and saute until the leeks are tender, about 5 minutes. Stir in the wine.
5. In a small bowl, stir together the broth and cornstarch, then add to the mushrooms and leeks. When the sauce is simmering and thickened, stir in the sour cream, lemon juice and tarragon.
6. Season the sauce with salt and pepper. To serve, spoon the sauce over the chicken breasts.
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