Cut the chilies into thin rings. Remove one-third of the chilies and set aside for garnish. Place the remaining chilies, garlic, sugar in a mortar and pound into a wet paste. (If you don't have a mortar, just chop with your knife.) Transfer to a small bowl and add the water, lime juice and fish sauce. Stir well to disolve. Add the reserved chilies and carrots. Set aside for 10 minutes before serving.
Mai writes: Nouc Cham is a must at every Vietnamese table, no matter what is served. You can use this condiment for dipping meat, seafood and vegetables, and for drizzling on rice. ... Although it will keep up to two weeks in the refrigerator, Nouc Cham is best when freshly made.