"White (square) on (the) right” or “white (square) to the right” is a chess rhyme for setting up the chessboard. A light-colored square (usually white) must be on each player’s far right-hand side.
“White to the right” has been cited in print since at least 1907 and “white on the right” since at least 1960.
Wikipedia: Rules of chess
Popular phrases used to remember the setup, often heard in beginners’ clubs, are “queen on her own color” and “white on right”. The latter refers to setting up the board so that the square closest to each player’s right is white (Schiller 2003:16–17).
October 1907, The Chess Amateur, pg. 39:
Remember—White to the right!
Take your chessboard and place it before you as if for the commencement of a game, that is, with a white square at your right-hand corner of the board—“White to the right.”
Place the chessboard in position—“White to the right.”
9 March 1950,
Q. Has it always been the custom to place a chess board with a white square at the right-hand end? I. S. R.
A. This custom was not firmly established until the latter part of the 15th century. Some authorities believe that it is of great antiquity, arising from the old Greek idea that white on the right insured good luck. Others, howeverm contend that the custom is neither very old nor of Greek origin, but is based on the extended powers of the queen.
16 July 1960, The Illustrated London News, pg. 126:
Consequently there is no rule to the effect that each player should have a white square at his right-hand side (again, we are merely retaining the old custom; the first mention of this “white on the right” rule is in a book by Dreissen in 1522).
("Dreissen" is a guess and is nearly illegible, as is the date—ed.)
Google News Archive
11 January 1969, The Leader-Post (Regina, Sask.), “Library has answers,” pg. 18, col. 8:
Q. In the game of chess what does the axiom, “white on the right” mean?
A. “White on the right” tells the players the correct positioning of the board. Two diagonally opposite corners of the board have white squares and two have black squares. Each player must have a white corner on his right side.
Chess: A New Introduction
By John Love
New York, NY: Scribner
An easy way of remembering this is: ‘White on the right.’