Recent advances towards the loss reduction in silicon nitride (SiN) has increased its interest as a material platform compatible with complementary metal-oxide-semiconductor (CMOS) processing [1]. SiN offers a large transparency range reducing multiphoton absorption processes, yet its nonlinear Kerr coefficient remains about 10 times lower than that of Silicon. Now, the new coming challenges in the development of optical integrated devices rise the need for highly nonlinear CMOS-compatible optical platforms based on hybrid waveguide structures. Hereafter we report on the properties of nonlinear hybrid SiN waveguides with a Ge 23 Sb 7 S 70 (GSS) chalcogenide glass cladding of layer thickness comprised between 100 and 200 nm. Using a bi-directional spectral broadening based method, we demonstrate that hybrid SiN waveguides with a 200 nm thick GSS cladding reach an effective nonlinear refractive index n2=0.8±0.2⋅10−18m2/W close to that of Silicon ( n2=2⋅10−18m2/W ), but without noticeable TPA.