The prerequisite for an efficient electron-positron gamma ray laser, which is the rapid formation o f a dense electron-positron plasma in a time shorter than the time for pair annihilation, is ideally fulfilled in a relativistic electron-positron superpinch. Because the cross section for annihilation decreases quadratically with the center o f mass energy, the time requirements otherwise imposed, are greatly relaxed. A relativistic electron-positron pinch can collapse under a complete population inversion into a very dense state possessing the form o f a long filament, just as it is required for a gamma ray laser. The gamma ray energies are the total center of mass energies, which can be much larger than the electron-positron rest mass energies.