1. Poach chicken: Place chicken in pot just large enough to hold it with about 3 inches of room on top. Add water and cover by 1 inch. Add peppercorns, parsley, thyme, bay leaf, carrot, celery, and salt. Bring water to just under a simmer over medium-high heat (bubbles should start forming around edges of pot and rise to surface, but there should be no bubbles in center of pot). Reduce heat to medium-low to keep temperature constant (it should be between 170 degrees and 180 degrees). Cook, skimming foam from surface as necessary, until an instant-read thermometer inserted in the thickest part of the breast registers 160 degrees, 15 to 18 minutes after the liquid reaches the right temperature.

2. Strain and cool: Transfer chicken to heatproof bowl. Strain liquid and pour over poached chicken; let cool in liquid (this will keep the chicken moist and tender). When chicken is cool, or you are ready to serve it, separate meat from bones and discard skin and bones. Slice chicken against the grain into 1-inch pieces, if desired.