Wrapping the fish in banana leaves makes this dish more authentic. They are big, so you will only need one or two.
Season fillets with salt and pepper. Place 2 slices of lime on each fillet and spoon chutney over the top; press gently.
If using banana leaves, cut away center ribs and set aside to use as ties for the packages. Cut six 8-by-10-inch pieces from leaves. Quickly pass each piece over a gas flame to soften. If using parchment, cut six 8-by-10-inch pieces.
Place a prepared fillet in the center of each banana leaf or parchment piece. Wrap each fillet securely and tie with the banana-leaf rib or kitchen string.
Fill a large pot with 1 1/2 inches of water. Place a steaming rack in the pot or a bamboo steamer over it. Bring to a boil. Arrange packages on rack or in steamer, making sure that packages do not touch. Cover; steam until fish is flaky and cooked through, about 14 to 16 minutes. Serve immediately.