Chosen is a companion quest in Elex and is connected to Berserker Caja who has unusual magic powers. Caja can join your team rather easily and when she does that, you can go with her and search for more Elex deposits.
How to unlock this quest: Speak with Caja in Domed City.
Caja stays in Domed City and she can accost the hero during your exploration of the city. Tell her about your good intentions and agree to meet her near the entrance to the city. When you get there, you can officially invite her to your team (1500XP) and start helping her in searching and analyzing new Elex deposits. When you express your interest in that you will be automatically moved near the first deposit.
Warning – Be sure that you are well-prepared every time when you are about to move to a new Elex deposit because they are guarded by enemies and each new group is stronger than the previous one.
The first deposit is located on top of a hill, north from Domed City. There, you can find a mutant and a group of Rotboars (those, that don't have Clumsy in their name are stronger). Try to attack them one by one, you can also try to lure single enemies away from the deposit.
When the battle is over you can get on the hill with the deposit. Caja must meditate in that place. Allow her to do that and wait until the process is completed (200XP + a bottle of Small Elex Drink found nearby – another 100XP).
The existence of another deposit is revealed to you when you make enough progress in the main story. The deposit is located at the west edge of Edan (west from Small Camp), near one of World Hearts. There, you must speak with Caja about Elex side effects. From now on, you can give her Mana (you can find a few units nearby) and for that you will get 100XP.
Go with Caja to the World Heart. A group of Biter monsters can be found in the area, lure them one by one away from the World Heart. The Night Shade monster should be the last one left. Use blocks or dodges because this monster deals a lot of damage. After defeating the monster, you can continue your journey to the World Heart. When you get there, allow Caja to meditate again. When she is done, you can speak with her (200XP).