position of the peak and deserve further scrutiny. A detailed comparison of this model to our data will be presented in a subsequent paper. In any case, we believe that for a proper prediction of χ$_{3}$ ( ω, T ) close to T$_{g}$ , a theory of supercooled liquids able to account for dynamical correlations is required. To conclude, we have provided the first direct experimental evidence that a supercooled liquid responds in an increasingly non-linear way approaching the glass transition. By measuring the frequency dependent third harmonics response χ$_{3}$ ( ω, T ) to a periodic electric field, which is tightly related to the dynamical correlation length, we showed that the number of correlated molecules increases as T decreases towards T$_{g}$ , confirmed the validity of previous estimates, and found that χ$_{3}$ scales as a function of ωτ . This opens a new path for probing the spatial correlations in both fragile and strong supercooled liquids and in the aging regime of glasses and spin-glasses, by systematic studies of non-linear responses. Future investigations along these lines might help to unveil the possible critical nature of the glass transition. We thank R. Tourbot for realizing the experimental cell, P. Pari for cryogenics, S. Naka- mae for her careful reading of the manuscript. We acknowledge interesting discussions with C. Alba-Simionesco, A. Lef` evre, R. Richert, M. Tarzia, and support by ANR grant DynHet. Acknowledgements ∗ Electronic address: francois.ladieu@cea.fr, denis.lhote@cea.fr [1] J.C. Dyre, Rev. Mod. Phys. 78 , 953 (2006). [2] P.G. Debenedetti, F.H. Stilinger, Nature 410 , 259-267 (2001). [3] M.D. Ediger, Annu. Rev. Phys. Chem. 51 , 99 (2000). [4] R. Richert, J. Phys.: Condens. Matter 14 R703 (2002). [5] U. Tracht et al. , Phys. Rev. Lett. 81 , 2727 (1998). [6] L. Berthier et al. , Science 310 , 1797 (2005). [7] G. Biroli, et al. , J. Chem. Phys. 126 , 184503 (2007). [8] C. Dalle-Ferrier et al. , Phys. Rev. E 76 , 041510 (2007). [9] See the discussion on this prefactor (called χ$_{0}$ ) following Eq. (18) in Ref. [7]. [10] K. Binder, A.P. Young, Rev. Mod. Phys. 58 , 801 (1986). [11] L.P. L´ evy, Phys. Rev. B 38 , 4963 (1988). 10