A covering of parchment paper helps retain moisture in this lovely thyme-scented chicken. Serve the sliced meat in the leek-and-thyme poaching broth, or chilled in a chicken salad.
Heat oil in a medium stockpot over medium heat. Cook garlic and leeks for 3 minutes. Raise heat to high. Add stock and peppercorns. Bring to a simmer.
Cut out a circle of parchment the size of the pot. Reduce heat to low. Add thyme. Season chicken generously with salt, and submerge in broth. Place parchment on surface of broth, and cover pot with lid. Poach chicken, flipping halfway through, until cooked through, about 15 minutes. (Broth should never simmer.) Remove and discard thyme if desired. Slice chicken, and serve in broth or on its own.