Heat butter in a large skillet until it begins to foam. Season thighs with salt and pepper. Add thighs to the skillet and brown on one side, approx 7 minutes. Turn thighs over and cook until well browned. The thighs are done when firm to the touch and juices run clear. Transfer thighs to a heated plate and cover with foil to keep warm.
Add shallots to the skillet and sauté until softened but not browned, approx 3 minutes. Lower heat. Remove skillet from burner and add brandy. Return skillet to the burner and let the brandy evaporate over low heat.
Add wine to the pan, raise heat to high, and bring to boil. Whisk in mustard and let reduce for 1 minute. Pour in chicken broth and cook for 2 to 3 minutes more.
Stir in cream and bring to boil. Immediately stir in chives and lower heat. Return thighs to the skillet and gently simmer until sauce has reduced and thickened slightly, approx. 4 to 5 minutes.
To serve, place 1 chicken thigh in the center of plate and spoon sauce over the top. Serve immediately.