Place water, chicken, ginger, chilis, mushrooms, fish sauce, lemongrass, Splenda and salt in a large saucepan.
If you have access to galangal, this is when you would use it instead of ginger. I addressed why you might choose to do this in the full post.
On high heat, allow the soup to come to a boil, and then lower to medium heat. Add in the coconut milk and stir. Let the soup simmer on for 10-15 minutes.
Stir in lime zest, lime juice and the rest of the fish sauce.
Serve with springs of cilantro and lime wedges.