How to Make It
In a shallow bowl, whisk the flour with a generous pinch each of salt and pepper. Season the chicken breasts with salt, then dredge them in the seasoned flour, shaking off the excess.
In a large skillet, melt 2 tablespoons of the butter in the olive oil over moderately high heat until the butter is foaming. Add the chicken and cook, turning once, until golden brown outside and white throughout, about 10 minutes. Transfer the chicken to a plate and cover with foil.
Add the bacon to the skillet and cook over moderately high heat, stirring occasionally, until just crisp, about 4 minutes. Using a slotted spoon, transfer the bacon to a plate lined with paper towels.
Add the shallot, garlic and thyme to the skillet and cook over moderately high heat until fragrant but not browned, about 30 seconds. Add the mushrooms and a generous pinch each of salt and pepper and cook over moderate heat, stirring occasionally, until browned and softened, about 7 minutes.
Carefully add the Marsala wine to the skillet and bring to a boil, scraping up any browned bits with a wooden spoon. Cook over moderate heat until reduced by half, about 5 minutes. Add the broth along with chicken breasts and any accumulated juices and cook until the chicken is white throughout and the pan juices have thickened, about 5 minutes. Swirl in the remaining 1 tablespoon of butter, then stir in the parsley, chives and reserved bacon. Serve.