Vladimir Vladimirovich Nabokov, author of the famous chess novel The Defense (also known as Luzhin's Defense) was a composer of chess problems. Nabokov's Poems and Problems (1969) includes 18 chess problems composed by the author along with 39 of his poems translated from the Russian and 14 poems that he wrote in English.
See Nabokov's amazing synesthesic chess problem on Etienne's blog:
http://blog.chess.com/Etienne/amazing-nabokov-chess-problem
"...inspiration of a quasi-musical, quasi-poetical, or to be quite exact, poetico-mathematical type, attends the process of thinking up a chess composition of that sort. ...it is one thing to conceive the main play of a composition and another to construct it. The strain on the mind is formidable; the element of time drops out of one’s consciousness altogether: the building hand gropes for a pawn in the box, holds it, while the mind still ponders the need for a foil or a stopgap, and while the fist opens, a whole hour, perhaps, has gone by, has burned to ashes in the incandescent cerebration of the schemer. The chessboard before him is a magnetic field, a system of stresses and abysses, a starry firmament. The bishops move over it like searchlights. This or that knight is a lever adjusted and tried, and readjusted and tried again, till the problem is tuned up to the necessary level of beauty and surprise. How often have I struggled to bind the terrible force of White’s queen so as to avoid a dual solution! It should be understood that competition in chess problems is not really between White and Black but between the composer and the hypothetical solver (just as in a first-rate work of fiction the real clash is not between the characters but between the author and the world), so that a great part of a problem’s value is due to the number of ‘tries’—delusive opening moves, false scents, specious lines of play, astutely and lovingly prepared to lead the would-be solver astray. But whatever I can say about this matter of problem composing, I don not seem to convey sufficiently the ecstatic core of the process and its points of connection with various other, more overt and fruitful, operations of the creative mind, from the charting of dangerous seas to the writing of one of those incredible novels where the author, in a fit of lucid madness, has set himself certain unique rules that he observes, certain nightmare obstacles that he surmounts, with the zest of a deity building a live world from the most unlikely ingredients—rocks and carbon, and blind throbbings."--from Speak Memory, Nabokov's autobiography ((http://www.cwrl.utexas.edu/~howard/314lspring2006/chess.html (Nabokov and Chess))
WHO CAN LIST A CHESS PLAYERS-POETS, AS WELL?
PUSHKIN.
LERMOMNTOV.
WHO ALSO?