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I'm not sure what the easiest way to do this is, but here's how I finally accomplished it, months after asking the question.
I'm not 100% certain that the final blow needs to be dealt before any of the enemies are damaged at all, but it worked that way, and I seem to recall it not working when I had already partially damaged them in the past.
The Damage Dealer
My most powerful damage-dealer is still Iron Man. He's been upgraded to 4 stars, and has some pretty serious Iso-8 crystals. I realized that Coordinated was messing things up by reducing the Chitauri's health with counter-attacks, so I swapped out a couple crystals to temporarily get rid of Coordinated. This left him with 3843 attack and 4110 accuracy. The crystals I swapped in gave him Veiled, which gives Stealthy at the start of the battle. This increases a hero's attack by 20%.
The area-attack ability I used was Laser Cutter, upgraded to 3 stars.
Finding the Battle
The task mentions three possible missions: 3.4, 3.2 (Hard), or 3.5 (Heroic). Obviously, we want to do it on the easiest possible difficulty to increase the chances of one shot killing everybody at once. However, doing it on 3.4 (Normal) proved impossible.
On normal, the first battle of 3.4 is against Minions of Thanos, and the rest of the battles are against the Church of Truth, so only the first battle even can have Chitauri. But, the only wave with three enemies includes Kronans. I'm not sure if Kronans count as Chitauri or not, but it doesn't matter because they don't die the first time their health is brought to zero. This means that you can't realistically kill both of them and the one Chitauri with a single attack.
The first wave of battle 3-2-6 on mission 3.2 (Hard) does indeed consist of three Chitauri. To get to this battle, take the left at the first fork. It's the only battle in the mission against Minions of Thanos. It may be possible on 3.5 (Heroic), but I didn't check since I was able to do it on Hard.
The Rest of the Team
In addition to the damage dealer, you want some allies to help him out.
The hardest part about this is that you have to start the battle with an Allied hero. Since you can't see what abilities your allies have assigned to their heroes before the battle starts, use one you're familiar with, or one that has a helpful Tactical ability (which can't be unassigned). For instance, Star Lord can give Focused to your damage dealer, and Black Widow can give Wide Open to an enemy.
As for the other heroes from your own roster, pick ones that can help out. I used a Wasp with Drone Swarm to Intimidate the enemies, lowering their defense and evasion.
The Fight
If any enemies are going to go before your damage dealer is ready to fire, and your allied hero has Coordinated, or might counter attack on their own (like Iron Fist or Star Lord), then swap them out for somebody else useful from your reserves.
The three Chitauri consist of two Blasters and one Tactician. Since Iron Man is a Blaster, he's weak against Tacticians. This caused my attack to fail to kill the Tactician the first time I tried it. Therefore, the Tactician (or the Blasters, if you're using a Bruiser for some reason) is a good target for debuffs, like Black Widow's Wide Open.
Use your heroes to set up the strongest shot possible, even if you have to take a couple hits from the Chitauri before firing. This is what I did, in whatever order the heroes' turns came in:
Use Wasp to Intimidate the enemies (reduced defense and evasion)
Use Wasp to Inspire your team (increased attack and accuracy)
Use Star Lord to give Iron Man Focused (increased accuracy)
Use Laser Cutter to kill them all.
Using Star Lord was risky because he may have used I Have A Plan to fire at one of the Chitauri, but I couldn't get a good allied hero and he was my backup. In retrospect, it would have been better to bring my Spider-Woman, even though she's only level 15. She could have given Iron Man Confident, which gives a huge boost to attack and accuracy for one shot.
This resulted in 100% Devastating hits that annihilated the Chitauri.
If things get screwed up at some point, like if you accidentally counter-attack, just Retreat. You'll lose the power you spent to start the battle, but that's less than the power spent on the first two battles to get here, or on the rest of the battles in the mission in order to start it over.
