Place chicken in a pot just large enough to hold chicken breast halves and add enough water to cover by 1-inch.
Add carrot, celery, parsley, thyme, bay leaves, peppercorns, and salt.
Bring just to a simmer over medium-high heat where bubbles start forming around the edge of the pot. Reduce to medium-low to keep temperature constant, about 170 to 180 degrees.
Cook, skimming foam from the surface until they reach 160 degrees on an instant-read thermometer, 15 to 18 minutes.
Transfer to a heatproof bowl and strain the liquid over the chicken and let the chicken breasts cool. This will keep them moist and tender. Refrigerate until ready to use, up to 3 days.
Separate meat from the bones and cut as desired.