It is correct and usable in written English.
You can use it when you are ending a section of writing. For example: With this thought, I am closing the chapter on my experiences in Spain.
But the mystical intensity of his religious scenes and the joyous abandon of his secular subjects form a triumphant closing chapter to 18th-century central European painting.
Eatock's aptly titled chapter 6, "Apotheosis," and closing chapter 7 explore Mendelssohn's lasting legacy in England and its subsequent effect, both positive and negative, on his reputation.
I hope that during the Secretary's closing chapter at the Interior Department he'll consider writing three addendums to all that he's accomplished.
But she nonetheless knows full well the duty of her position; "I have written this book because I am lucky to have a public platform and want to use it," she writes in Secrets closing chapter.
Calling the closing chapter "Animal Civilization" is unhelpful.
This huge reshuffle marks the closing chapter of a love affair that turned sour.
They nevertheless contain archaeological significance and accidental eloquence, which Fox unfolds beautifully in her closing chapter.
Ellis ran out of dart; Shaun Perry came on and had an unfortunate closing chapter.
By the time the reviewer reaches the book's closing chapter, confirmation bias has solidified.
The closing chapter, 6-4 for Nadal, left Roddick spent and disillusioned.
Mr. Kennedy's closing chapter and his afterword explain what makes it so.
