2-3 tablespoons lime juice, plus 4 thin lime slices for garnish
1-2 teaspoons fish sauce, or reduced-sodium soy sauce
2 scallions, trimmed and sliced
¼ cup fresh cilantro leaves
1Trim lemongrass stalks of root ends, outer leaves and grassy tops. Cut into 2-inch lengths. Smash each piece with the flat of a chef's knife. Crush ginger and garlic (do not peel) with the knife. Trim stems from chiles, cut in half lengthwise and smash (for maximum heat do not remove the seeds).
2Place the crushed lemongrass, garlic, ginger and chiles in a wide pan and pour in broth. Bring to a simmer, skimming off any foam that rises to the surface.
3Add chicken breasts to the broth. Cover and simmer gently over low heat just until the chicken is cooked through, 10 to 12 minutes. With tongs, transfer the chicken to a cutting board and set aside.
4Bring the broth to a lively boil and boil for about 5 minutes to intensify the flavors. Strain the broth into a saucepan, pressing on the solids to extract all the juices. Stir in coconut milk and heat through over medium heat.
5Stir together cornstarch, 2 tablespoons lime juice and 1 teaspoon fish sauce (or soy sauce) in a small bowl. Add to the soup and cook, stirring, until simmering and slightly thickened, 2 to 3 minutes.
6Thinly slice the poached chicken and add to the soup. Season with additional lime juice and fish sauce (or soy sauce) to taste. Ladle the soup into bowls and float a lime slice, some scallions and cilantro leaves in each one.
Make Ahead Tip: Cover and refrigerate for up to 2 days.
Ingredient Note: Lemongrass is an aromatic tropical grass used to add a pungent, lemony flavor to Asian dishes. It is available fresh at large supermarkets and Asian groceries.
People with celiac disease or gluten-sensitivity should use soy sauces that are labeled "gluten-free," as soy sauce may contain wheat or other gluten-containing sweeteners and flavors.