We have used the molecular beam growth technique, which we call cleaved edge overgrowth, to fabricate highly efficient lasers that operate in the 1D quantum limit. The active region of our laser consists of atomically precise quantum wires that form at the T-shaped intersections of 7 nm wide GaAs quantum wells grown along the (001) and, after an in situ cleave, along the (110) crystal axis. The origin of the quantum mechanical bound state is the relaxation of quantum well confinement at this intersection, which leads to an expansion of the electron and hole wavefunction into the larger available volume at the T-junction. The high degree of structural perfection achievable in this way allows the observation of stimulated optical emission from the lowest exciton state in optically pumped devices. The interpretation that the observed quantum wire response is due to exciton recombination is based on the near spectral constancy of the emission over almost three orders of magnitude in excitation power from low-power luminescence to a single-mode lasing line. The implied absence of bandgap renormalization effects suggests that the Mott density is never reached and indicates interesting new behaviour of excitons in 1D. In contrast, the quantum well photoluminescence peak indeed shifts to lower energies consistent with the notion that the 2D excitons ionize and a free electron-hole plasma forms.