  The ignition of Quantum Cascade Lasers can occur from a state of oscillating
fie ld domains. Here, the interplay between lasing and the kinetics of
traveling dom ain boundaries provides complex oscillation scenarios. We analyze
our numerical findings in detail for a device operating at terahertz
frequencies and manifest chaotic evolution by positive Lyapunov exponents. This
shows that these importan t devices can exhibit chaotic behavior even without
periodic driving, which need s to be taken into account in their design.
