Discard any excess fat from the chicken fillets and cut them in half lengthways. Combine the brown sugar, lime juice, curry paste and 2 of the kaffir lime leaves, shredded, in a bowl. Add the chicken and mix well. Cover and refrigerate for several hours or overnight.
Trim the lemon grass to measure about 20 cm (8 inches), leaving the root end intact. Cut each lengthways into four pieces. Cut a slit in each of the remaining lime leaves and thread one onto each skewer. Cut two slits in the chicken and thread onto the lemon grass, followed by another lime leaf. Repeat with the remaining lime leaves, chicken and lemon grass. Pan-fry or barbecue until cooked through.
To make the mango salsa, put all the ingredients in a bowl and stir gently to combine. Serve with the chicken skewers.