In a medium saucepot, heat water and 1/4 tsp. salt to a low simmer. Add chicken and cook 5 minutes. Remove from heat and let chicken stand in cooking water 7 minutes. Drain and set aside to cool completely.
Meanwhile, to make dressing, combine lemon juice, mustard, tarragon, and remaining 1/4 tsp. salt. Whisk in olive oil until blended.
When chicken has cooled, slice pieces crosswise into 1/4" thick strips. Place chicken in a large bowl, add the grapes and celery, and stir in dressing. Just before serving, mix in pecans. Serve, if desired, on top of salad greens.