1) Dissolve 1 tbl. salt in 3 cups cold water in medium saucepan. Submerge chicken in water. Heat over medium heat until water registers 170 degrees. Off heat, cover saucepan and let sit until chicken registers 165 degrees, 15-17 minutes.
2) Transfer chicken to paper towel-lined plate and refrigerate until cool, about 30 minutes. Pat chicken dry with paper towels and cut into 1/2" pieces.
3) Whisk mayonnaise, lemon juice, and mustard together in medium bowl. Add chicken, celery, shallot, and parsley and toss to combine. Season with salt and pepper to taste, and serve.
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