  A detailed quantum-electrodynamic calculation of muon pair creation in
laser-driven electron-positron collisions is presented. The colliding particles
stem from a positronium atom exposed to a superintense laser wave of linear
polarization, which allows for high luminosity. The threshold laser intensity
of this high-energy reaction amounts to a few 10^22 W/cm^2 in the near-infrared
frequency range. The muons produced form an ultrarelativistic, strongly
collimated beam, which is explicable in terms of a classical simple-man's
model. Our results indicate that the process can be observed at high
positronium densities with the help of present-day laser technology.
