A primer bonded to some kind of shaped propellant bonded to a projectile.
The chamber would act as the case. Of course it would require a new ejector scheme as there would be noting to eject but the primer.
H&K worked on that idea for years and *almost* had their design fielded by West Germany as the replacement for the G3. As Travis noted, heat-soak was a problem (the H&K ammo used a chemical primer and firing pin, but the priming compound was modified for heat resistance. IIRC, it needed a double priming charge, too - the second (larger) priming charge acted to squirt the projectile out of the propellant block (it was encased within). I don't recall whether there was any primer component remaining after ignition... I suspect it was designed so that the primer itself would be consumed in the propellant burn.
I believe the W. German government was funding that program, too - and German Reunification (and it's tremendous costs) forced the German military to scrap those plans. Perhaps it is just as well, there's no way that such ammunition could ever be crafted in someone's garage. Caseless rifle ammo might already have been the NATO standard now for years, had the Berlin Wall not fallen when it did. And we'd have been deprived of military surplus brass long ago.
I hadnt consider the thermal coefficient of brass