Bring water, onion, thyme, chile, peppercorns, and garlic to a gentle simmer in a medium pot. Add chicken, and simmer until cooked through, about 8 minutes. Transfer chicken to a plate, and let cool slightly.
Bring poaching liquid to a boil, and cook until reduced to 3 1/2 cups, about 10 minutes. Strain through a fine sieve into a medium saucepan, pressing on solids to extract liquid. Discard solids.
Bring liquid to a boil. Add barley, and simmer until liquid is absorbed and barley is tender, 30 to 40 minutes. Transfer to a large bowl, and let cool.
Shred chicken into bite-size pieces. Toss with barley, scallions, vinegar, oil, salt, and pepper. Gently stir in figs, and serve immediately.
Store-bought fig-balsamic vinegar lends a mellow, mildly acidic tang to anything. Use it whenever you'd reach for standard balsamic, whether with farmers' market greens, grilled meat, or fresh berries.