1. Place chicken in a small saucepan and cover with water; bring to a boil. Cover, remove from heat, and let stand 15 minutes. Drain, cool, and coarsely chop chicken.
2. Combine chicken, apples, celery, and pecans in bowl; toss gently to coat.
3. Whisk together mayonnaise, sour cream, mustard, tarragon, salt, and pepper. Pour dressing over chicken mixture; toss gently to coat. Cover; chill at least 30 minutes.