In 4qt or larger, heavy-bottomed pot, begin heating chicken broth and coconut milk on low-medium heat.
Add the other ingredients for the broth, down through the brown sugar, as you prepare them.
Bring broth to a slow simmer; never allow it to reach a rolling boil, and do not cover it at any time during cooking.
When broth 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 cilantro-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 before adding the cilantro.
About a minute after adding the cilantro, taste the soup and add some additional lime juice as desired to punch up the flavor (maybe 1-2 T-don't overdo it!).