The epigraph to the chapter tells us that there's no such thing as the beginning of a story, so we get the idea that, even though this is the beginning of the novel, other things have been going on.
Daniel Deronda is at a gambling resort watching a young woman at the roulette table. He's trying to decide whether or not she's beautiful.
The narrative jumps back in time, but just a little, to show us how he got there and why he's looking at this girl.
Fifty or sixty people are either gambling or watching others gamble; we get a few descriptions of some of them. It's a pretty diverse crowd (for nineteenth-century Europe, we mean).
All of a sudden Daniel feels his attention captured by a young lady who is gambling (the one who he's not sure is beautiful or not). She's not someone who would necessarily make people stop and admire her, but she's not someone you can ignore, either.
The young lady wins a round of roulette and collects her money. As she looks around her, she and Daniel lock eyes.
When their eyes meet, we shift from Daniel's perspective to the young woman's. She wonders how long they've been looking at each other. She feels weird about it. She doesn't know him.
The young woman loses the next round, and the narrator comments that Daniel's gaze had somehow acted as an evil eye that jinxed her.
She loses the next round, too. She's pretty sure that Daniel is still watching her.
The young woman's chaperone tells her that they should stop playing, but she decides to ignore this and keep gambling. We find out that her name is Gwendolen. She figures that "since she was not winning strikingly, the next best thing was to lose strikingly" (1.8).
Gwendolen keeps playing round after round, and every time she loses one round she doubles her stake on the next. Everyone is watching her, but she's only aware of Daniel (but she never looks up at him).
Gwendolen ends up losing all of her money; she looks at Daniel, who has a "smile of irony in his eyes" (1.8).
We learn that Daniel is "young, handsome, distinguished in appearance" (1.8). We also learn that the paragraphs in this book tend to be very long.
That evening, a bunch of people get together. Gwendolen is looking sharp in "sea-green robes and silver ornaments, with a pale sea-green feather fastened in silver falling backward over her green hat and light-brown hair" (1.10). She's with the same lady she had gambled with before, as well as a "gentleman with a white mustache and clipped hair: solid-browed, stiff, and German" (1.10).
A bunch of men start making observations about Gwendolen. Mr. Vandernoodt says he thinks her pretty. Mr. Mackworth says he can't endure the look of her mouth. The unnamed dowager (basically, a widow who gets all of her husband's goods) says that she doesn't think Gwendolen is pretty at all.
We find out that the man and woman that Gwendolen's hanging out with are a baroness and a baron, and their last name is Langen.
Mr. Vandernoodt goes to talk to them.
People have been commenting that Gwendolen looks kind of like a serpent. We learn that she's been twisting her neck in every which way because she's on the lookout for Daniel.
Gwendolen asks Mr. Vandernoodt about who Daniel is. He tells her that he has come to their hotel with Sir Hugo Mallinger, and that his name is Daniel Deronda. She's like, "Oh, my, what a delightful name!"
Mr. Vandernoodt asks if she's interested in Daniel. Gwendolen says she is.
Vandernoodt says he will introduce them and asks the baroness, who goes by Madame von Langen, if it's OK. She says it's OK.
As the chapter ends, we learn that Gwendolen will not actually meet Daniel at this event, and that when she gets back to her hotel room she receives a letter instructing her to come home.