Yeah, that's a lace monitor (aka tree goanna), and it is more than capable of eating a decent sized chicken. They can get quite large, up to 2m in length. They are predatory carnivores and birds form a very significant portion of their diet. They're called tree goannas for good reason.
As for being venomous, that's a question that is still being debated. They have dental glands that excrete proteins, which is a lot more like snakes and their venom glands than they are like us with our salivary glands, but exactly what function those proteins perform is still being researched, and that is why the question of whether or not it qualifies as venom or is just a nasty form of saliva is still up for debate.
That's irrelevant to this anyway, as a large lace monitor vs a chicken, the monitor doesn't need venom to bring down its prey. It's bite force alone is enough to end most birds, and their mouthful of I think about 60 teeth are like razors. If bitten by one, the bite is going to bleed, a lot. Some people blame the "venom", but it doesn't contain procoagulants like brown snake venom does, so that's a bit of a misnomer. We all know the sharper the blade, the more bleeding when cut with it, and that's exactly the case with the teeth of monitor lizard teeth. There's no way to overstate how viciously sharp their teeth are.
It was probably an evolutionary leftover from a time when such lizards possibly were venomous, or maybe they started to evolve venom and never made it all the way there because they didn't end up needing it. The idea that they could be venomous is a bit scary, and for some reason people love to latch onto scary things and spread the story, and that's exactly what has happened with this lizard family and the discovery that they had dental glands that released proteins... looks like venom, works like venom - except that it doesn't, therefore it is really venom? The answer to that is in the hands of scientists and herpetologists far more qualified than I'll ever be, but I'm not going to be surprised if in the end it's all a fuss about nothing.
They also eat carrion, so their mouths can be dirty with bacteria and disease, which is more likely to bring down a prey item than those "venom" proteins will. Again, another reason why the venom speculation doesn't hold up so well.
As for feeding habits, yes, they will absolutely hunt and kill chickens, or any other bird for that matter, but they rarely kill prey and abandon it. They don't kill for fun like cats do, they don't go on killing sprees like foxes do, and they're not human, so they tend to only kill what they want to eat. The only time they'll leave a body behind is if they get disturbed and have to flee before they get to eat their catch, and with something like a chicken, it's just as likely that they'll run away with it in their gob and carry it up the tree with them. They can swallow prey items whole like snakes do, but they can also rip and tear flesh and eat things in chunks, I've seen them chowing down on roadkill kangaroos, so it's not as if it would have killed a chicken then found it too large to eat.
So why would there be other chickens deceased in the pen but not eaten? Well, normally it's the job of a rooster, but when none are around, sometimes a hen will behave a bit like a rooster and take it upon herself to try and protect the flock. If the lizard is trying to catch one hen and some of the other hens are attacking him for it, that could be a good reason for him to bite multiple hens. And as I mentioned before, their bite force alone is enough to bring down most birds. Also, as mentioned before, their bite can potentially carry disease. If he was feeding on a wild bird that had bird flu, then went running around a pen full of chickens, it wouldn't even need to directly harm the chickens, it would only need to drink from their water supply to spread bird flu, which can spread and kill a small flock rather quickly. Obviously, he also did eat at least two of them, and bit at least one more, but the ones with no marks on them... might be still the lizard's fault, but might not be the result of a direct attack. The question also has to be asked, how did it get in? If it could get past the fence, so could a fox, or a cat, it might not have been just the one predator. Foxes are cunning buggers, they sometimes follow other predators around to take advantage of the strengths and abilities - and leftovers - of those predators.