Place the chicken in between 2 squares of cling film and flatten, using a rolling pin. This will help the chicken cook quicker and evenly.
Season the chicken with salt and pepper.
Heat a pan or skillet over medium-high heat and the olive oil. Once it's hot, add the chicken and cook until it's golden brown on both sides.
Remove the chicken from the pan and set it aside.
Deglaze the pan with white wine scraping up any browned bits from the bottom. This liquid will help create a flavorful sauce.
Add the butter, then the shallots and sauté until they become soft and translucent.
Add the garlic and chopped tarragon. Stir and cook for 2 minutes.
Add the heavy cream and let it simmer until it thickens slightly. If you prefer a lighter version, you can omit the cream and use chicken broth for a lighter sauce.
Return the cooked chicken to the pan and simmer in the sauce for 5 minutes to allow the flavors to meld. Make sure the chicken is heated through.
Cook in the oven for 10 minutes at 200C/400F degrees.
Serve the tarragon chicken hot, with a drizzle of the creamy tarragon sauce over each piece.