Place chicken on a plate and sprinkle all over with flour.
Reserve the excess flour.
Heat 2 tbs 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 tbs 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.
Ready in 35 minutes.