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Season the chicken with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Add the chicken and sauté for 3 to 4 minutes. Add the shallots and sauté for 1 minute.
Turn the breasts over and add the white wine. Place the lid on the skillet, turn the heat down to low and simmer for another 5 minutes until the chicken is done, which is when it feels firm to the touch and a meat thermometer inserted in the center reaches 170°F.
Transfer the chicken breasts to plates. Bring the liquid to a boil; add the chicken stock, cream and fresh tarragon. Simmer for 2 to 3 minutes until sauce has slightly thickened.
Pour the sauce over the chicken and give a final scattering of tarragon to serve.