Pare very thinly the bright-colored rind from the limes (no white). Blot the peel on paper towels to remove any excess oil. Put peel in a 4 cup screw-top jar. Add 2 cups of the rum. Close the jar. Store in a cool, dark place for 2 days or until rum has absorbed the flavor. Remove the peel and add the sugar. Shake vigorously until the sugar dissolves and add remaining cup of rum. Close jar and store in a cool, dark place at least 1 month to age.