In a bowl, combine the lemongrass, chilli, garlic and fish sauce. Place the chicken meat into another bowl and add half the lemongrass mix, reserving the rest. Cover and place in the fridge to marinate for at least 20 minutes.
Heat the oil in a wok or a large non-stick frying pan over a high heat. Add the reserved lemongrass mixture and stir-fry for about one minute until fragrant. Then add the marinated chicken and stir-fry for 4-5 minutes, or until the chicken pieces have a nice colour on all sides. Add the broccoli and stir-fry for another minute.
Pour the chicken stock into the pan and stir in the sugar. Simmer for a few minutes, or until the stock has reduced and you are left with a thick sauce. Serve with steamed rice and garnish with the herbs.