Prepare the Marinade: In a medium bowl, whisk together the olive oil, lemon zest, lemon juice, chopped tarragon, minced garlic, salt, pepper, chicken broth, and Dijon mustard until well combined.
Marinate the Chicken: Place the chicken breasts in a shallow dish or a resealable plastic bag. Pour the marinade over the chicken, ensuring they are well-coated. Allow the chicken to marinate for at least 15 minutes (or up to 1 hour if you have the time).
Cook the Chicken: Heat a non-stick skillet over medium-high heat. Once hot, remove the chicken from the marinade (reserving the marinade) and place the chicken breasts in the skillet. Cook for about 5-6 minutes on each side, or until the chicken is golden brown and cooked through.
Add the Marinade: Once the chicken is cooked, carefully pour the reserved marinade into the skillet. Let it simmer for 2-3 minutes, allowing the sauce to reduce and thicken slightly.
Serve: Transfer the chicken breasts to a serving plate, drizzling the sauce over the top. Garnish with additional fresh tarragon leaves and serve with lemon wedges on the side.
Notes
For best results, marinate the chicken for up to 1 hour.