Separate the celery stalks. Rinse the celery, pat dry with paper towels. Chop the stalks and leaves into 1-inch pieces, cutting the stalks on the diagonal.
Preheat the wok on medium-high heat and add oil. When the oil is hot, add the chopped garlic, chilies and the Chinese celery. Stir fry until the Chinese celery starts to turn a darker green (about 2 minutes), splashing with the rice wine or sherry while cooking.
Add the soy sauce, sugar and 1 tablespoon of the chicken broth. Continue stir-frying until the Chinese celery is tender but not soft, adding the remaining 1/2 tablespoon chicken broth if needed. Serve hot.