Trim the brown tips from the fiddleheads, if desired. Bring a large pot of salted water to a boil. Add the fiddlehead ferns, reduce heat to medium, and cook until just tender, about 2 minutes. Drain the fiddleheads and plunge into cold water. Drain again and set aside.
Scoop off 3 - 4 tablespoons of the coconut "cream" from the top of the opened can and place in a large pot. Heat over medium high heat. When the coconut cream begins to bubble, add the shallot, ginger, garlic and curry paste. Cook, stirring occasionally, for 5 minutes.
Add the chicken and carrots and stir again. Reduce the heat to medium-low and cover. Simmer for 15 minutes, stirring from time to time, or until the carrots are barely tender. Stir in the fiddlheads and cook for another 5 minutes, or until the fiddleheads are hot.
Stir in the lime juice, sugar, fish sauce and salt. Simmer for a moment, then taste and adjust seasonings to taste.
Serve with jasmine rice and sprinkle with fresh basil leaves and sliced chives, if desired.