Put the chicken breasts in a large saucepan and add water to cover. Season with 1 t salt. Bring just to a boil; reduce heat and simmer 10 to 15 minutes or until cooked through. Remove chicken from water and cool. Dice and put in large bowl.
While chicken is cooking, toast the almonds in a skillet set over medium heat. Time 5 minutes or just until the almonds are beginning to turn golden. (Alternatively, toast almonds in a 350-degree oven for 15 minutes.) Let cool and coarsely chop.
Mix together mayonnaise, yogurt, 2 T lemon juice, salt and pepper to taste. Fold into the chicken, Stir in the thyme, celery, green onions and grapes. Cover and refrigerate several hours to chill and blend flavors.
Just before serving, dice the nectarine and toss with the other tablespoon of lemon juice. Fold the nectarine and almonds gently into the salad.