You can poach the chicken a day ahead and serve it cold; it is delicious in salads and sandwiches. The poaching liquid can be reserved as a base for soup or frozen for up to three months.
Place stock, parsley, thyme, garlic, bay leaf, peppercorns, 2 teaspoons salt, the carrots, and chicken in a pot. Add enough cold water to cover by about 1/2 inch.
Clip a candy thermometer to side of pot. Heat over medium-high heat until temperature of the stock reaches 170 degrees (liquid should be moving beneath the surface but no bubbles should appear). Cook, adjusting heat to keep the liquid between 170 degrees and 180 degrees and the surface still, until an instant-read thermometer inserted into thickest part of chicken breast registers 165 degrees, 18 to 24 minutes.
Using a slotted spoon, remove chicken from liquid. Let stand until cool enough to handle. Remove skin, and cut breast along bone to remove meat in one piece. (Chicken can be covered partially with broth and then topped with parchment paper and refrigerated overnight.)
Slice chicken crosswise. Divide chicken and carrots among 4 plates. Spoon 1 tablespoon poaching liquid and 2 tablespoons salsa over each chicken breast, and season with salt if desired.
To avoid straining, tie the herbs and peppercorns in cheesecloth.