1. Preheat oven to 350°.
2. Discard giblets and neck from chicken. Tie ends of legs together with twine. Lift wing tips up and over back; tuck under chicken. Place chicken, breast side up, in oven bag; seal bag according to package directions. Cut 4 (1/2-inch) slits in top of bag. Place bagged chicken in a 13 x 9-inch metal baking pan. Bake at 350° for 1 1/2 hours or until drumsticks move easily. Remove chicken from bag; discard bag and cooking liquid. Place chicken on a cutting board; let stand 10 minutes. Discard skin and bones. Cut chicken into 1/2-inch pieces. Cover and chill at least 30 minutes.
3. Combine wine, shallots, 1/2 teaspoon salt, and pepper in a small saucepan; cook over medium heat until liquid is absorbed. Combine shallot mixture, remaining 1/2 teaspoon salt, yogurt, mayonnaise, and tarragon in a medium bowl; cover and chill.
4. Add chicken and onion to mayonnaise mixture; stir to combine.