This paper describes a field experiment of stress measurement using the overcoring method performed in a rock slope, called Rochers de Valabres (located in France's Southern Alps Region), a field laboratory site prone to rockfalls. Six measurements were conducted at shallow depths from the surface, moving deeper along a sub-horizontal borehole. The experiment was conducted in heterogeneous and anisotropic gneiss, with the overcored rock elastic properties, as evaluated by biaxial and uniaxial tests, being widely scattered. Since stress calculations are sensitive to all input data uncertainties, strain inversion was, thus, performed using an experimental device and Monte Carlo simulations. The experimental device allows the assessment of rather broad confidence intervals for both stress magnitude and orientation. The results indicate that the stress state in the surface area is quite heterogeneous and may be correlated with topography. The measurements show a nonlinear stress distribution with distance to the free surface, along with high values of principal stresses, despite the vicinity of the surface. Although influenced by local topography, orientations of the principal computed stresses are characterized by a high turnover due to local heterogeneities. The results are roughly in accordance to a 2D finite element model of the site.