This review is fairly safe to read if you haven't read the book (i.e., it doesn't give away any major plot points or twists in the story) but offers an interpretation for those who have.

Mr Turner is a British war veteran who has lately been having fainting fits. He goes to see a specialist called Mr. Hughes who tells him that there are pieces of shrapnel from an old war injury lodged irretrievably in his brain and that, as a consequence, he doesn't have long to live. He begins to think about what he would like to do with his remaining time and reminisces about the hospital where he initially received treatment for his wound. He remembers the three patients he shared a ward with: two Englishmen — a commando wanted for murder, a snobbish pilot with an unfaithful wife — and an American — a black man who has slit his own throat and also stands accused of rape. When he realises he doesn't know what happened to them he decides to find out and, with the assistance of his somewhat sceptical wife, to see if he might be able to help them in some way. It's a simple premise but one that Shute uses to build a complex narrative of interlocking stories.
The Chequer Board manages to address racial tension, considers and compares Buddhism alongside Christianity, and successfully depicts something of British character, all in under 300 pages. It must have been a somewhat unconventional book upon its publication in 1948.