Preheat oven to 350 F. Sprinkle chicken with salt and pepper. In large oven-proof sauté pan with tight fitting lid, heat olive oil and butter over medium heat until butter is melted. Add chicken and sauté for 6 – 7 minutes, or until browned. Turn and repeat.
Add leeks and carrots and cook, stirring well, for another 1-2 minutes. Add tarragon and chicken stock. Bring liquid to a boil, remove from heat and cover. Place pan in oven and braise for about 40 minutes, or until an instant read thermometer registers 170 F.
Remove pan from oven. Place chicken and vegetables on a platter and cover with foil. Bring liquid in braising pan to a boil on stovetop. Boil and reduce for about 5 minutes. Add cream and stir for another minute. Return chicken and vegetables to sauté pan and gently stir to combine, spooning over chicken. To serve, arrange chicken and vegetables on platter and spoon sauce over.