The Imperial Library

After acquiring the second piece, Ria Silmane made another visit:

"I would congratulate you on retrieving the second piece of the Staff of Chaos, but dire portents have I seen. The third piece of the Staff lies somewhere in the Elden Grove, ancient home of the Elves. The Elden Grove is said to be the birthplace of the sacred First Tree, that which gave life to all the forests on the continent of Tamriel. Its location has been a closely guarded secret, so guarded in fact that many believe that even the Elves have forgotten its true location. Considering that there are only three provinces that hold any of the Elven people, your search should not be too difficult. Find the Elden Grove and recover the third piece of the Staff. I wish you well on your quest..."

The place is located in Valenwood province. To finally get the location of Elden Grove, the Eternal Champion had to get a gem called the Heart of Selene. This gem is important to defeat Selene, High Priestess of Shagrath, the God of Spiders. The gem is located in her lair - Selene's Web. The champion had to infiltrate the lair and liberate the gem. After delivered the gem, the Elves of Eldenroot then agreed to share the location of Elden Grove.

 
"The small overgrown entrance to the Elden Grove stands before you, guarding secrets forgotten for ages.
Somewhere within its misty corridors lies the third piece of the Staff of Chaos."

After acquiring the third piece, the Eternal Champion had to face Jagar Tharn's image again:

"Why do you choose to align against me when it is obvious that I will destroy you. Even as each piece of the Staff comes into your possession it becomes easier to find you, and I have done just that. Face my creatures, if you dare. I am through toying with you..."

As the previous encounters, the Eternal Champion defeated Jagar Tharn's minion. After some rest, he was ready for the next.