Place chicken breast in stock pot and fill pot with water until water is just covering chicken breast.
Add lemon peels and bay to pot and place on stove burner. Place pan lid on pan, positioning at an angle to allow steam to escape. Turn heat to high and bring pot to boil.When water reaches rolling boil, immediately turn pan down to barely a simmer. Continue to cook over low simmer for 10 minutes. After 10 minutes turn heat off, leaving pan on burner.Allow chicken to rest for 20 minutes in hot water. This will complete the cooking process slowly, allowing the chicken to cook slowly and evenly, ensuring a moist breast.
While chicken rests, chop tarragon and green onions for the salad.
Chop the tarragon herb using only 3 chops, this preserves the flavor of the tarragon herb.
Chop green onion tops, leaving the rounds in tact. Discard the green bottoms
Remove chicken from stockpot after the 20 minute resting time and slice into 1/3 inch thick pieces.
Add chopped tarragon, green onions, mayonnaise, salt, pepper and sliced chicken into medium mixing bowl. Shred chicken with 2 forks. The poached chicken should come apart easily with this method.
As you shred, pull the other ingredients in the bowl into your mixture. Keep forking until you reach your desired consistency. I prefer a fully shredded chicken salad with tarragon, but if you like your chicken salads chunky feel free to stop when you are satisfied with the texture. I hope you enjoy this simple, flavor forward chicken salad recipe!