Place chicken on a plate and sprinkle all over with flour. Reserve the excess flour.
Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add the chicken and cook, turning once, until browned on both sides, 4 to 6 minutes total. Transfer to a plate and cover with foil to keep warm.
Add the remaining 1 teaspoon oil, leek and mushrooms to the pan. Cook over medium-high heat, stirring often, until the vegetables are tender, 6 to 8 minutes.
Sprinkle the reserved flour over the vegetables and stir to coat. Add broth, wine and salt and bring to a simmer. Return the chicken to the pan and simmer, turning the chicken occasionally, until it is cooked through, 4 to 6 minutes. Stir in tarragon.
Tips for Two: Chicken BrothStorage: Leftover canned broth keeps for up to 5 days in the refrigerator or up to 3 months in your freezer. Leftover broths in aseptic packages keep for up to 1 week in the refrigerator.Uses: Add to soups, sauces and stews; use for cooking rice and grains; add a little when reheating leftovers to prevent them drying out.