Fill a Dutch oven two-thirds full of water; bring to a boil.
Wrap each chicken breast half completely and tightly in heavy-duty plastic wrap. Add the chicken to boiling water. Cover and simmer for 20 minutes or until a thermometer registers 165°. Remove from pan, and let stand for 5 minutes. Unwrap chicken and shred; refrigerate for 30 minutes or until cold.
Combine mayonnaise and the next 7 ingredients (through black pepper) in a large bowl, stirring with a whisk until combined. Add chicken, 1/3 cup celery, cranberries, and almonds; toss well to coat. Cover and refrigerate for 1 hour. Serve over salad greens.
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