Lightly season the chicken on both sides with salt and pepper, then coat with the flour, shaking off any excess.
In a large skillet, heat the 2 tablespoons olive oil over medium-high heat. Add the chicken and cook until golden and cooked through, 3 to 4 minutes on each side. Transfer to serving plates to rest.
Add the shallots to the skillet and cook until just translucent, about 1 minute. Pour in the wine and cook, stirring up the browned bits from the bottom of the pan, until reduced and syrupy, 1 to 2 minutes. Pour in the chicken broth and boil until reduced by half, about 2 minutes. Turn off the heat and stir in the butter and any juices from the resting chicken. Season the sauce to taste with salt and pepper and spoon over the chicken.