Place chicken breasts in a medium saucepan and cover with cold water by 1 inch.
Bring water to a gentle simmer over medium heat, skimming any foam from the surface.
Reduce heat to low, cover pan, and simmer 12 to 14 minutes until chicken reaches 165°F inside.⏱ 14 min
Transfer chicken to a cutting board and let cool completely for 15 minutes.⏱ 15 min
Cut the cooled chicken into bite-sized 1/2-inch cubes.
Whisk mayonnaise, Dijon mustard, lemon juice, salt, and black pepper together in a large mixing bowl.
Add cubed chicken, celery, scallions, fresh dill, and flat-leaf parsley to the dressing bowl.
Fold ingredients gently with a rubber spatula until the chicken is evenly coated.
Taste and adjust seasoning with extra salt or lemon juice before serving.