New propagation regimes for light arise from the ability to tune the dielectric permittivity to extremely low values. Here we demonstrate a universal approach based on the low linear permittivity values attained in the epsilon-near-zero (ENZ) regime for enhancing the nonlinear refractive index, which enables remarkable light-induced changes of the material properties. Experiments performed on Al-doped ZnO (AZO) thin films show a six-fold increase of the Kerr nonlinear refractive index (n2) at the ENZ wavelength, located in the 1300 nm region. This in turn leads to ultrafast light-induced refractive index changes of the order of unity, thus representing a new paradigm for nonlinear optics.The nonlinear optical response of matter to light is, by its very nature, a perturbative and hence typically weak effect. Applications, e.g. for nonlinear optical switches or quantum optics, are therefore largely underpinned by the continuous endeavour to attain stronger and more efficient light-matter interactions. Nonlinear mechanisms can typically be classified as resonant or non-resonant, depending on the frequency of light with respect to the characteristic electronic resonances of the material. Non resonant nonlinearities, like those present in transparent crystals or amorphous materials (e.g. fused silica glass), are generally weak and require high light intensities and/or very long samples to take advantage of an extended light matter interaction. Conversely, resonant nonlinearities can be several orders of magnitude stronger, but this comes at the price of introducing detrimental losses. A typical example is that of metals, which both reflect and absorb light strongly [1][2][3]. An alternative approach to enhance the nonlinear response of a material consists of creating artificial electromagnetic resonances, for example by stacking materials of different refractive index or using other types of composite materials [4][5][6][7][8][9][10][11]. Creating resonant metaldielectric stacks and composites yields a very strong nonlinear enhancement [12][13][14], but inevitably exacerbates the detrimental role of linear and nonlinear losses. Here we propose a different approach to enhance the effective nonlinearity without resorting to optical resonances. Our approach relies on enhancing the nonlinear effect, measured in terms of the nonlinear Kerr index n 2 , rather than on a direct enhancement of the intrinsic χ (3) nonlinear susceptibility. As we show below, this enhancement arises due to the fact that the nonlinear refractive index is a function of both the nonlinear susceptibility and the linear refractive index. Recent progress in material design and fabrication has provided access to the full range of linear optical properties bounded by dielectric and metallic regimes. Of particular relevance for this work are materials which exhibit a real part of the dielectric permittivity that is zero, or close to zero, such as transparent conducting oxides where their permittivity cross over is typically located in the near infrared s...