The book was published in 1976 (although the last game in it was played in 1971), and the top 12 players (according to Chernev) were
An interesting list, and one I think that some people have objected to over the years. I recall the suggestion that Chernev's hero worship of Capablanca resulted in his No 1 ranking, and almost as a flow on effect, Alekhine at No. 2.
Of course a modern list would have to include Kasparov in the top 2 or 3, and Fischer's legend has grown since the original publication of the book. In fact most people I've discussed this topic with seem to think a top 4 of Alekhine, Capablanca, Fischer, Kasparov (although not in that order) seems to pick itself, with various choices for player 5. Karpov is often overlooked in this debate, while positional players all seem to plump for Botvinnik. However I'm inclined to give Chernev his due in one regard, and make Lasker my choice for no 5 in the list of "5 Greatest Chess Players".
Without running a full blown poll, feel free to add your own lists in the comment section.