Add the butter and garlic to the pan and continue cooking for 4-5 minutes until fragrant. Add the tarragon, mustard, lemon juice and wine to the pan. Allow to simmer for about 2 minutes, until most of the wine has evaporated.
Stir in the cream and allow to simmer for 5 minutes. Add the chicken back to the pan and allow the sauce to thicken for about 10-15 minutes, basting the chicken breasts a few times. Check that the chicken is cooked through. Season to taste before serving.