Bring chile, corn kernels, coconut milk, and water to a boil in a medium saucepan. Reduce heat, and simmer until corn is tender, about 20 minutes.
Filling a blender halfway and covering with a kitchen towel, puree soup in batches. Strain through a coarse sieve into a large bowl; discard solids. Season with salt and pepper.
Chill soup at least 3 hours or up to overnight. Stir in lime juice. Garnish each serving with fresh corn kernels if desired, and season with pepper.