That's hard enough as it is. But Walter Abish attempted a much more difficult task in his 1974 book, Alphabetical Africa.
In Chapter 1, only words beginning with A are allowed.
Here's the Google Books preview so you can see what that looks like. The first sentence of the book is:
"Ages ago, Alex, Allen and Alva arrived at Antibes, and Alva allowing all, allowing anyone, against Alex's admonition, against Allen's angry assertion: another African amusement... anyhow, as all argued, an awesome African army assembled and arduously advanced against an African anthill, assiduously annihilating ant after ant, and afterward, Alex astonishingly accuses Albert as also accepting Africa's antipodal ant annexation."
In Chapter 2, the rules are the same, except now B-words are allowed along with the A-words. In Chapter 3, C-words become usable; D-words are allowed in Chapter 4, and so on, until finally, in Chapter 26, the entire English language becomes open for business.
Until Chapter 28, when Z-words are again disallowed after two glorious chapters of being acknowledged. Chapter 29 sees Y-words removed from play, X-words in Chapter 30, until in the final chapter, Chapter 52, we're back to A-words only, like an alphabetical Flowers for Algernon.
Abish didn't entirely pull it off. People have noticed places where he used disqualified words. In fact, quite a few places. Stephen Saperstein Frug has compiled some 50 screwups, most commonly early O's (usually 'of' or 'or') and late W's (coming in the couple chapters after W's are supposed to come off the table). One screwup comes on page 2, an early I in the form of the word 'in'. It really could have used some extra time at the editor's desk to catch some of these errors; reportedly, Abish was shocked when told that he hadn't entirely pulled it off. That said, Abish did do enough to show that such a book was possible. Not exactly War and Peace, but a valid book.
Not that I wager anyone out there is keen to try and beat his mark themselves.