1 pound boneless, skinless chicken breasts (about 3), cut into 2 1/2-by-1/4-inch strips
3 tablespoons Asian fish sauce (nam pla or nuoc mam)
1 1/2 tablespoons lime juice
1 quart plus 3/4 cup canned low-sodium chicken broth or homemade stock
3 stalks lemongrass, bottom third only, peeled, smashed, and cut into 2-inch pieces, or three 3-inch-by-1/4-inch strips lemon zest
1 1-inch piece peeled fresh ginger, cut into thirds
1/2 cup long-grain rice
1 3/4 cups unsweetened coconut milk (15-ounce can)
2 fresh red chiles or jalapeño peppers, seeds and ribs removed, cut crosswise into thin slices
3 tablespoons chopped cilantro