Take a wok, and put coconut milk, begin heating coconut milk on low-medium heat for 1 minutes.
Bring liquid to a slow simmer; never allow it to reach a rolling boil, and do not cover it at any time during cooking.
When soup is simmering, begin adding remaining ingredients starting with the chicken, as you prepare them in the order listed, stirring regularly.
Make sure the chicken is fully cooked by the time you add the lime juice--if you cube the chicken finely enough and use a normal length of time preparing the vegetables, this should not be an issue, but allow it to simmer a few extra minutes if necessary.
About a minute after adding the lime juice, taste the soup and add some additional lime juice as desired to punch up the flavor (maybe 1 Tspoon-don''t overdo it!).