The phrase "on the first chapter" is correct and usable in written English.
You can use it to refer to the first chapter in a book, series, or other long works. For example, "The author introduces a key character in the first chapter, so I'm eager to see how the story develops."
He's spent the past year on the first chapter, and in honor of Bloomsday, he'll offer up a summary of it tomorrow.
Linda Kate Bensonn), a graduate student in philosophy, has been working on the first chapter of her dissertation on Immanuel Kant for four years.
If Dickens had spent the same time on each word, he'd still be working on the first chapter of Pickwick Papers.
"You cannot call the Iron Curtain the 'Ferrous Veil'!" he badgers his wife, the long-suffering Beth (Mare Winningham), insisting on giving her notes on the first chapter of a detective novel she's writing.
Now the collaborative group Elevator Repair Service — which has made quite a splash with its adaptation of Fitzgerald's masterwork "The Great Gatsby" — has taken on the first chapter of Faulkner's heartbreaking 1929 novel, "The Sound and the Fury".
He set down almost none of his doctrine in writing, with the exception of a short text that seems to be only a fragment: his commentary on the first chapter of the Zohar—"Be-resh hormanuta de-malka"—as well as commentaries on isolated passages of the Zohar that were collected by Ḥayyim Vital, who attests to their being in his teacher's own hand.
He spent much of the 1950s writing Catch-22, having gained a contract with the publisher Simon & Schuster on the basis of the first chapter.
On the first page of the first chapter of her first novel, "Major Pettigrew's Last Stand," Helen Simonson invites her readers to experience love at first sight.
It is so fundamental to winning that it is on the first page of the first chapter of the Predator's Guide.
One of the more interesting and comprehensive parts of the first chapter focuses on Karl Popper insofar as he is a founder and leading advocate of "natural-selection epistemology".
As the leader: Hand out sheets with questions on it for the first chapter and a pen for each person.
