Intrigue and world-building galore!
First of all, I echo a sentiment from another comment somewhere that the initial "fight" scene is a bit difficult to follow, which is strange because it's pretty graphic. I think the issue is that in an attempt to make the throat cutting scene brief, we're left with weird placement of the bodies in the room. I'm not a skilled assassin by any means, but it usually SEEMS like a good throat-cutting happens with the assailant surprising the victim from behind (or maybe I've watched too much TV?). When the scene is described with the attacker shoving the body backwards, it sounds like the attacker is standing in front of the priest, which makes sense because then we also get a description of the priest's eyes as his throat is being cut.
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To make things simpler, so that readers don't get confused as they try to visualize what's going on, all it would take is a word here or there to straighten it out. The attacker could be moving forward as he slashes at the priest so that when he shoves the priest backward, it's not like "Wait, what?" Because my automatic assumption is that the attacker has come at the victim from behind to do the evil deed. I understand there are stylistic reasons why the author has done the opening paragraph the way he has, but if the following paragraphs are overly confusing, the risk is losing the readers attention immediately.
That said, I loved my glimpses into this world. I have only read the first chapter, however, so things I might say here could be addressed in the next chapter.
I loved the names in the story, the sense of the larger world, like the Chop, that just sounds fantastic. The House of Humboldt is a great name too, and Little Mille, etc. I loved all this stuff. The Machine was actually the weakest name. It works, of course, I'm just saying that it pales in comparison to the other fantastic ones so far.
Which, speaking of names, I'm not sure why the character we're following in the first chapter isn't given a name yet. For me it makes the story clunky, but perhaps this is addressed later on. I do think there should be a really really good reason to not name a character the first time we meet them. Even Brandon Sanderson names Szeth the first time we see him slaughter an entire wedding party (if my memory serves me).
There's some really great description going on, and excellent details, which definitely make me want to read more. Keep writing and posting! Can't wait to see how much this develops!