This is a Thai-style soup, versatile and very easy to make. You can substitute shrimp for the chicken, or use a combination of chicken and shrimp. If you don't have Kaffir lime leaves or fish sauce, the soup will still be good. The broth can be made ahead (without the chicken and garnishes), and reheated at serving time. Add the chicken at the last minute so it stays moist and tender.
Combine the stock, coconut milk, lemongrass, ginger, pepper, chile sauce, garlic, fish sauce, and lime leaves, if using, in a medium-size pan. Bring to a simmer over medium heat, then reduce heat to low, and simmer 15 minutes. Don't allow the mixture to boil. Turn off the heat, cover the pan, and let the broth steep for 30 minutes.
Strain the liquid into a clean pan and discard the solids. At this point, the broth may be refrigerated, covered, up to 3 days.
Slice the chicken crosswise into 1/2-inch strips, then cut these in half lengthwise. You want all the strips to be about the same size so they cook evenly.
Reheat the broth over medium heat to the start of a simmer (don't boil). Add the chicken and gently poach the meat until cooked through, about 5 minutes.
Stir in the lime juice and season with salt, as needed. Divide the soup into warm bowls and garnish each serving with a sprinkling of basil and cilantro. Serve piping hot.