Cut unpeeled pineapple lengthwise into quarters. With a small, sharp knife, cut between flesh and peel of each quarter to release fruit in 1 piece; reserve shell. Trim core from fruit and discard. Cut fruit into 1/2-inch chunks and place in a large bowl.
Cut chicken into 1/4-inch-thick strips 2 to 3 inches long. Add chicken and grapes to pineapple in bowl.
In a small bowl, whisk sour cream, lemon juice, wine, and sugar until smooth. Stir in chopped mint. Pour dressing over fruit and chicken and mix to coat. Add salt and pepper to taste.
Set each pineapple shell, cut side up, on a dinner plate. Spoon 1/4 of the chicken salad into each shell, letting excess spill onto plate. Garnish with mint sprigs, if desired.