We report the first experimental observation of the route to chaos for semiconductor lasers with weak optical feedback. For increasing feedback level, the laser undergoes a quasiperiodic route interrupted by frequency locking, which is also predicted by a comprehensive numerical analysis. Experiments further demonstrate the occurrence of quantum-noise-induced transitions between two attractors with different relaxation oscillation frequencies. The attractors are created by two subsequent Hopf bifurcations of the same external cavity mode.