Season chicken thighs with ½ teaspoon tarragon, ½ teaspoon salt and ¼ teaspoon black pepper. In a medium skillet, heat the olive oil over medium-high heat. Sear the chicken, skin side down, until the skin is brown and crispy, about 3 to 4 minutes.
In a 4 to 6 quart slow cooker, combine the baby red potatoes, mushrooms, carrots, onions, and garlic. Season with remaining tarragon, salt, and black pepper.
Pour in the chicken stock and white wine. Add the seared chicken on top of the vegetables. Cover and cook for 4 hours on high or 8 hours on low until chicken is done and vegetables are tender. Chicken is done when a meat thermometer inserted in the center reaches 180°F. Add peas for the last five minutes of cooking time.
To serve, place a chicken thigh in a shallow bowl. Surround with vegetables. Pour the white wine sauce around the chicken and vegetables.