Rinse chicken thighs and pat dry. Remove and discard any excess fat. Cut chicken into 1/4-inch-thick strips 2 to 3 inches long.
Rinse lemon grass. Cut off and discard tough tops and root ends; peel off and discard tough, outer green layers of stalks down to tender white portion of bulbs. Finely chop tender portions; you should have 5 to 7 tablespoons.
In a bowl, mix chicken, lemon grass, 2 tablespoons fish sauce, sugar, and garlic.
Set a 10- to 12-inch frying pan over high heat; when hot, add oil and shallots and stir until shallots begin to brown, about 1 minute. Add chicken mixture and stir until chicken is no longer pink in the center (cut to test), about 3 minutes.
Stir in broth and sliced chili to taste; bring mixture to a boil. Taste, and add more fish sauce if desired. Spoon into a serving dish and sprinkle with cilantro.