There have been a lot of attempts at designing 3 dimensional chess, but what about going the other way. There is at least 1 version of 1-D chess, played on a ring, as well as variations on a theme, where the boards are almost 1-D.
I'm not sure how playable such games are, although the rules seem to make sense. There is no queen (doesn't quite fit, although it could still be R+B), and the knight seems crippled. On the other hand the bishop moves are logical.
One test is to get two 1-D chess engines to play each other and see what sort of games occur. If there is an obvious winning strategy (or the games look stupid) then it is of course a bust!
If you are interested in giving 1-D chess a try then the rules for each of these games can be found here.