Place chicken breasts in a large pot and cover with salted cold water. Bring to a boil, reduce heat to low and simmer until chicken is cooked through, 8 to 10 minutes. Remove to a cutting board to cool. When cool enough to handle, dice.
In a small bowl, whisk together mayonnaise, parsley, lemon juice, honey and 1/4 tsp. salt.
In a large bowl, combine chicken, apple, celery, onion and almonds. Add dressing and toss well. Cover and chill for 1 hour. Toss chicken mixture with greens and serve.