Heat oven to 375°. Heat oil in a 6-qt. saucepan over medium-high heat. Season chicken with salt and pepper; working in batches, cook chicken, flipping once, until browned, about 10 minutes. Transfer chicken to a plate; set aside.
Add shallots and garlic to pan, cook, stirring occasionally, until golden, 3-5 minutes. Add wine, stock, mustard, and thyme; bring to a boil.
Return chicken to the pan with any juices, cover with a lid, and transfer to the oven. Bake until chicken is cooked through, about 45 minutes, or until an instant-read thermometer inserted into the thickest part of the thigh reads 165°.
Transfer chicken to a serving platter and keep warm. Return saucepan to stove; bring to a boil. Cook, stirring occasionally, until reduced by half, 8-10 minutes. Spoon sauce over chicken; garnish with tarragon.
