In a bowl, combine the goat cheese with chopped tarragon and season with salt and pepper.
With a sharp knife, cut a slit in the side of each breast to form a pocket. Stuff each breast with goat cheese mixture and seal with a toothpick.
Salt and pepper the breasts.
Heat olive oil and butter over medium-high heat in a sauté pan with enough room for all 4 breasts. Sauté 4 to 5 minutes on one side until lightly browned.
Flip over and sauté an additional 3 to 4 minutes, or until the internal temperature of the meat (not the filling) reaches 165° F.
Transfer to a plate and cover with foil to keep warm.
Sauté shallots in olive oil for 3 minutes until translucent.
Deglaze pan with wine and reduce to an essence.
Add chutney, thyme, rosemary, chicken stock, roasted garlic and reduce until sauce is thick enough to coat a spoon.
Salt and pepper to taste.
Spoon sauce over chicken breasts and serve.