Much like climbing Mt. Everest because its there, some hypothetical molecules are just too tantalizing for chemists to resist attempting a synthesis. Thus in 1964, Edgar Heilbronner speculated on whether a conjugated annulene ring might be twistable into a Möbius strip. It was essentially a fun thing to try to do, rather than the effort being based on some anticipated (and useful) property it might have. If you read the original article (rumour has it the idea arose during a lunchtime conversation, and the manuscript was completed by the next day), you will notice one aspect of these molecules that is curious by its absence. There is no mention (10.1016/S0040-4039(01)89474-0) that such Möbius systems will be chiral. By their nature, they have only axes of symmetry, and no planes of symmetry, and such molecules therefore cannot be superimposed upon their mirror image; as is required of a chiral system (for a discussion of the origins and etymology of the term, see 10.1002/chir.20699).