In a medium saucepan, place the chicken breasts, parsley, thyme, celery, carrot and ¼ of the onion. Cover with cold water. Bring to a boil, lower heat and simmer for 15 minutes. The chicken is done when it feels firm to the touch and a meat thermometer inserted in the center reaches 170°F. Remove the pan from the heat, uncover and cool the chicken in the liquid for 30 minutes. Transfer the chicken to a cutting board and let rest for 2 to 3 minutes, until it’s cool enough to handle.