Combine the stock, lemongrass, chopped ginger, ½ chile, if using, and garlic in a saucepan and bring to a boil. Simmer for 15 minutes, then strain the stock. Reheat to a simmer with the julienned ginger.
While the stock is simmering, chop the chicken breast into ¼-inch dice (you can use a food processor for this, but be careful not to grind the meat too fine). Com