Using the multifractal approach, we derive the probability distribution function (PDF) of the velocity gradients in fully developed turbulence. The PDF is given by a nontrivial superposition of stretched exponentials, corresponding to the various singularity exponents. The form of the distribution is explicitly dependent on the Reynolds number. The experimental data are in good agreement with the PDF predicted by the same random beta model used to fit the scaling of the velocity structure functions. PACS numbers: 47.25. — c One of the fundamental features of three-dimensional fully developed turbulence is the non-Gaussian statistics at small scales. The energy transfer toward small scales is related to the nonzero skewness of the probability distribution function (PDF) of the gradients, and the large flatness of the PDF (kurtosis) corresponds to the presence of strong bursts in the energy dissipation. This is the most striking signature of the so-called intermittency phenomenon, responsible for the failure of the classical theory of Kolmogorov (K41) which neglects the presence of fluctuations in the energy transfer [1]. Recently, several papers [2-5] have discussed the PDF problem. A first approach [2-4] uses a new mappingclosure theory introduced by Kraichnan [2]. Starting from a Gaussian reference field, he introduced a mapping function J describing the squeezing ratio of the length scale. The evolution equation for J is obtained by modeling the dynamical processes present in the Navier-Stokes equations with a particular emphasis on the local selfdistortion of turbulent structures in physical space. A second method applied dimensional arguments in order to relate the small-scale Auctuations to large-scale statistics assumed to be Gaussian [5]. Thus, explicit forms of the PDF are derived in the context of the K41 theory and of the fractal beta model [6,7]. However, these forms are not consistent with the existing data. This Letter generalizes the approach used in Ref. [5] to the multifractal [6,8,9] case. In particular, we show that the random beta model [9] allows us to obtain good fits of both the scaling exponents of the structure functions and the PDF of the gradients. Let us brieAy recall the basic features of the multifractal description. In the following, we shall ignore the vectorial character of the quantities, as well as constants of order 1 in the equalities, which are unessential for our dimensional arguments. In the inertial range of lengths, the velocity increments P (Ir)dIr =I p(h)dh, (2) where p(h) is a smooth function of h which is independent of /. The scaling ansatz (2) implies that