XCOM 2

Story related

You will run into the chosen many times in missions where they'll harass you and try to kidnap your soldiers or extract knowledge to find the commander faster (which is bad news if they do you'll have to complete an annoying defend the avenger mission and if you lose it's game over)

On regular missions, you will have to either complete the objective or drain the Chosen's health bar to get rid of them on that particular mission but you can't kill him. To actually kill them, you will need to build the Resistance Ring building and start sending out your soldiers on covert missions to locate their stronghold that is the only place where they can die.

There are 3 covert missions for each of the Chosen called 'Hunt the Chosen: Part 1, 2, 3', you need a soldier of at least Sergeant rank for Part 1, a Lieutenant for Part 2 and a soldier of Major rank for Part 3. When you have successfully completed Part 3, you will be able to attack the stronghold and finally kill them.