In this paper, we investigate theoretically the stabilization of a free-running vertical-cavity surface-emitting laser exhibiting polarization chaos dynamics. We report the existence of a boundary isolating the chaotic attractor on one side and a steady-state on the other side, and identify the unstable periodic orbit playing the role of separatrix. In addition, we highlight a small range of parameters where the chaotic attractor passes through this boundary, and therefore where chaos only appears as a transient behaviour. Then, including the effect of spontaneous emission noise in the laser, we demonstrate that, for realistic levels of noise, the system is systematically pushed over the separating solution. As a result, we show that the chaotic dynamics cannot be sustained unless the steady-state on the other side of the separatrix becomes unstable. Finally, we link the stability of this steady-state to a small value of the birefringence in the laser cavity and discuss the significance of this result on future experimental work.Semiconductor lasers -or laser diodes -are small, efficient and cheap laser devices and therefore are widely used for industrial applications. To generate a chaotic output however, since they typically behave as damped oscillators, an external perturbation such as optical feedback or modulation is required 1 .But recently, it has been shown that some specific semiconductor laser structures -namely Vertical-Cavity Surface-Emitting lasers (VCSELs) -could generate chaotic polarization fluctuations without the need for an external forcing due to a competition between two modes in the laser cavity 2 . The specific dynamics of VCSELs has been studied intensively for more than 20 years 3-11 , and polarization chaos has only been observed once, recently and only in nanostructured devices. Yet the theoretical framework reproducing accurately the observed dynamics does not take the specificities of the nanostructures into account 5,6 , which therefore raises the question: why has this dynamics never been observed in standard, commercial VCSELs before? Here we provide some elements of answer to this question. We theoretically highlight the existence of a separatrix between the chaotic dynamics and a steady-state, and demonstrate that the noise easily pushes the system over this boundary which therefore suppresses the chaotic dynamics. Moreover, we show that this mechanism appears for a large range of parameters, and in particular when the birefringence of the laser cavity is small. Finally, we discuss the relevance of this result by comparing available experimental data between chaotic and stable devices, and show that the chaos suppression mechanism described here is coherent with experimental reports.