Place 1 litre water in a saucepan over high heat. Spear the chilli, garlic and ginger on a wooden cocktail stick or skewer (this makes them easy to remove later) and add to the pan together with the lemongrass. Bring to the boil and boil for 1 minute. Remove from the heat, cover and set aside to infuse for about 30 minutes.
Return the liquid to the boil, then reduce the heat to low. Add the chicken pieces, shallot and green beans, and poach for 12–15 minutes or until the chicken is cooked (test with the tip of a knife – the juices should run clear). Add the zucchini slices for the last 2 minutes of cooking.
Using a slotted spoon, transfer the chicken, beans and zucchini to a warmed bowl. Add a little of the poaching liquid to keep them moist, then cover tightly and keep warm.
Return the liquid to the boil and add the coconut milk, stirring until it dissolves. Continue boiling for about 5–6 minutes or until the liquid has reduced by about one-third.
Remove the chicken meat from the bones and shred it roughly. Return the chicken meat, beans and zucchini to the soup and stir, then reheat briefly. Stir in the grated lime rind and juice. Season with pepper.
Divide the chicken and vegetables among 4 soup bowls. Spoon over the liquid, discarding the lemongrass and stick of chilli, garlic and ginger. Sprinkle with the coriander and serve.