Better stats, troops and upgrades
This is the main building on your territory and it is a big one. The Chief's Hut is the "city hall" of this tribe and it requires more resources and time for upgrade. This will unlock then better stats, troops and upgrades. Whenever possible, I suggest you upgrade this first because it will greatly benefit the tribe. With a strong Chief the whole tribe's CP will go up and you will be able to do better game content as well as join better guilds (since some guilds have CP requirements). Before upgrading this, I suggest having all the other buildings at the maximum level possible since it will raise the level these buildings can have.