Chop 2 sprigs of fresh Tarragon and combine in bowl with 1 tsp salt, and 1/4 tsp ground pepper. Rub mixture all over chicken. Transfer to larger roasting pan, you can refrigerate this up to 24 hours before baking.
Put pineapple, chopped shallots, rice wine vinegar, sugar, and 1/2 tsp salt into food processor. Mix until slightly chunky.
Spread pineapple mixture over chicken and then add remaining Tarragon sprigs and sliced shallots to roasting pan. Bake chicken, basting with pan juices occasionally, until skin is golden, about 50 minutes.