(Inspired by an NPR program talking about how subatomic particles were detected)
The amount of matter at the birth of the universe was only slightly more than antimatter, on the order of one particle in a billion excess. Both formed galaxies, stars, planets, and eventually life. The civilizations discovered each other with some terrible accidents in the beginning but formed a truce, communicating via radio or laser. Eventually the cosmologists calculated that the matter universe could take over on sheer mass alone; thus began the war to annhilate the threat for good. The antimatter worlds, fighting for survival, carried out devastating kamikaze raids on major worlds and star clusters of the matter universe. This went on for millenia. The attacks reached the proportions of cosmic disasters on both sides before finally the matter universe was pressed to accept that while matter might be left at the end of the war’s natural conclusion, no matter-based spacefaring life would survive. Finally peace came again.
– romantic subplot: two radio operators on opposite sides fall in love. Aside from being completely unable to ever touch, they are of radically different physical forms.
(if anybody wants to turn this into an actual novel I am perfectly happy for them to do so if they give me credit for the idea)