The stationary 3D Euler equation describes an inviscid and incompressible fluid flow in equilibrium. V.I. Arnold proved in 1965 that a steady Euler flow exhibiting a chaotic behavior must be a Beltrami field, i.e., a vector field which is collinear with its curl. Beltrami fields also appear in the context of MHD equilibria, where they are known as force-free magnetic fields. The goal of this talk is to show that, with probability 1, a Gaussian random Beltrami field exhibits chaotic regions that coexist with invariant tori and knotted orbits of arbitrarily complicated topologies. The motivation to consider this question is Arnold's conjecture on the typical complexity of Beltrami fields. The proof is based on a nontrivial extension of the Nazarov-Sodin theory for Gaussian random monochromatic waves combined with different tools from the theory of dynamical systems, including KAM theory, Melnikov analysis and hyperbolicity. This is joint work with Alberto Enciso and Alvaro Romaniega.