The Red Brotherhood Hideout is a secret location, providing a hideout to the Red Brotherhood.
The location works much like the other hideouts of hostile minor factions, but contains a Qualis Gem in a chest on one of the rocks near the cave entrance. It only spawns once and, once taken, will never be there again.
The treasure chest is only lootable when you are in the hideout. If you have defeated all enemies and pressed Tab to leave without first looting the chest, you will have lost the opportunity. The contents of the chest do not appear in the hideout loot screen after pressing Tab.
The chest is lootable without defeating all enemies, so it is recommended that you clear a path to the cave and loot the chest as soon as possible. If you get defeated after looting the chest, you still keep the contents.
Reaching the chest for the Qualis Gem is possible in the early game with strong (level 30+) companions or troops (though defeating all enemies would be much more challenging).
After defeating all enemies, you will receive a message saying, "The thieves guarding the treasure were beaten - find the treasure chest." This is simply a reminder to find and loot the chest before pressing Tab, as the chest was lootable before this point.
In order to unlock this location, you must ask NPC travelers (such as Greydan and Jeran Longshanks) in taverns for information, to which they may offer a map to you for 200 denars. One of these possibilities is getting the map to the hideout.