Earlier in the morning I was talking with my partner about what was going on that day. As far as I knew, nothing. We were sitting in the room with our nieces, one talking one coloring. He said that he wasn't sure if he was going out, because my sister in law and my nieces were planning on going to pick up some new shoes and pick up some manga. I wanted to see if the new manga for Ikigami was out, so I asked if it would be ok to go with them. They said it was fine, of course, but I would have to endure getting new shoes first. I didn't really have an issue with it, so I took a shower, and we went.
So as we were going in, one of my nieces said told the other one that we were going "chez [name of store]." I stood there for a minute, amazed at the usage. First and foremost, it was a store. I had heard "chez" used before when referring to someone's house, but it's really amazing at how useful of a preposition it is. It generally means at someone's place.
Naturally, you can say "chez moi," meaning my place, but you can also say "chez boucher," meaning at the butcher's. Additionally, it can be used for a group. So you could say something like "chez les Bleus," which depending on context could mean any number of the stadiums of any national sports team in France. [Most typically used for football, but can just as easily be applied to rugby, handball, etc.] Additionally it can be used for customs, especially when they are peculiar to a culture. For example, "Chez les Français, on fait la bise." [In France, most people you greet will kiss you on both sides of the cheek, unless they don't know you or want to keep their distance. Then it's a handshake. I've found it's easiest to follow the other person's lead.]
It can also mean in the work/writings of someone. You could introduce something like "Chez Dumas . . . " meaning "In the works of Dumas . . . ." So this is a clever little announcer that might help you sound a little more native, depending on what you're discussing. I am not sure of it's level of formality, so it's on the watch list for now.
So I asked what the root was of "chez." Fairly obviously, it's Latin root is "casa." It means house, hut, or cottage depending on use. Most if not all Latin languages share the root. More specifically in meaning, "chez" comes to mean something where someone, or a group of people, has control over it. In using "chez" for a house, it's implying that it is relating to the person who has control over it.
"Chez moi" is more saying the place where I have control than specifically, "my house." If you wanted to generally say that it was your house, you would simply say "ma maison." In a way, you may be able to compare it to the difference between "house" and "home" in English.
Also, my niece has developed a taste for declaring the United States, "Le plus drôle pays du monde." I don't think it would be nearly as funny, were she not six.