Season chicken on both sides with 1/4 teaspoon each salt and pepper. Heat 1 1/2 teaspoons oil in a large heavy skillet over medium-high heat. Add the chicken and cook until well browned, about 3 minutes per side. Transfer to a plate and tent with foil.
Reduce heat to medium. Add the remaining 1 1/2 teaspoons oil to pan. Add shallots; cook, stirring, until softened, 2 to 3 minutes. Add broth and wine and bring to a simmer. Cook until reduced by half, about 3 minutes.
Return the chicken and any accumulated juices to the pan; reduce heat to low. Simmer until the chicken is cooked through, about 4 minutes. Transfer the chicken to a warmed platter. Stir mustard, sour cream and tarragon into sauce. Season to taste with salt and pepper and spoon over the chicken.
3 lean meat, 1 fat