Whisk together first 4 ingredients in a large bowl; stir in chicken and next 2 ingredients. Add salt and pepper to taste. Chill 3 hours. Stir in almonds just before serving.
Curried Chicken Salad: Omit shallots, tarragon, grapes, and almonds. Whisk 1/4 cup finely chopped green onions, 1 Tbsp. grated fresh ginger, and 2 tsp. curry powder into mayonnaise mixture. Stir 3/4 cup each golden raisins and diced yellow bell pepper into chicken mixture. Stir in 3/4 cup toasted sweetened flaked coconut and top with 1/2 cup chopped lightly salted roasted peanuts just before serving.
Poppy Seed Chicken Salad: Omit tarragon and grapes. Whisk 2 Tbsp. chopped fresh basil, 1 Tbsp. orange zest, 3 Tbsp. honey, and 1 tsp. poppy seeds into mayonnaise mixture. Stir 1 cup sweetened dried cranberries into chicken mixture. Stir in 1 cup chopped toasted pecans just before serving.
Mango Chicken Salad: Omit shallots, tarragon, grapes, and almonds. Whisk 1/4 cup diced red onion; 2 jalapeño peppers, seeded and minced; 3 Tbsp. chopped fresh cilantro; and 1 Tbsp. lime zest into mayonnaise mixture. Stir 1 1/2 cups diced fresh mango into chicken mixture just before serving.