The ingredient Painted Troll Fat comes from Painted Trolls, a rare form of troll that only exists in the Painted Forest entered during the quest A Brush with Death. Its alchemical properties are completely different from those of standard Troll Fat.
There are only six painted trolls (none of which respawn) and therefore it is only possible to get six samples of Painted Troll Fat. It cannot be duplicated in the Arch Mage's Enchanted Chest.
Its rareness is unfortunate, because otherwise it is a very powerful alchemy ingredient, with its unique combination of four valuable restorative effects.