Monochromatic chess is a fairy condition in which no piece
or pawn may move from a dark square to a light square, or vice versa.
This is a very severe restriction to normal chess: Knights cannot
move at all; Pawns can only capture (possibly after an initial double
step); and only K-side castling is legal.
Checks are fairy, i.e. a King is only in check by enemy
units standing on same-colored square, when capturing the King would
be a monochromatic move. So that e.g. the two Kings can be in contact.
The monochromatic constraint has been used several times in the popular
Sherlock Holmes book by
Smullyan. It lets you construct problems having a rich retro-content
without filling the board with many pieces. Certainly that is a sufficient
justification for this fairy condition !
Here is an example:
The Chess Mysteries of Sherlock Holmes,
6+4. Monochromatic chess. White to
Prove that a promotion and an en passant capture occurred
This genre is somewhat less restrictive than monochromatic chess and,
perhaps as a consequence, less used in retros.