Plasma confinement in toroidal devices may be significantly degraded because of flux surface destruction and consequent stochastic wandering of magnetic lines. In this study a model stochastic differential equation is considered which describes guiding center electron motion in a statistically specified spectrum of turbulent magnetic fluctuations. The fluctuation intensity is assumed to satisfy the Chirikov criterion (resonance overlap) for onset of stochasticity. In this limit typical lines diffuse and are adequately described by a quasilinear diffusion coefficient Dm. However, quasilinear theory does not describe an important mechanism for loss of particle correlations: Particles collisionally diffuse from one line to an adjacent one which diverges rapidly from the first, carrying the particles away. The scale length LK for line divergence is related to the inverse of the Kolmogorov-Sinai entropy. An attempt is made to determine LK from a simplified Eulerian vertex renormalization. The exponentiation length which emerges is LK ∼ Ls(k̄02Dm″ Ls)−1/3, where Ls is the shear length, k̄0 is a typical azimuthal wavenumber, and Dm″ is of order Dm. In a particular limit of weak shear, the particle diffusion coefficient can then be estimated as D ∼ Δr2/τc, where Δr2 ∼ Dmz (τc), z(τ) is the distance traveled along the lines in time τ, and for static fluctuations τc ∼ τ(Lδ), where Lδ is LK multiplied by a logarithmic factor involving the perpendicular collisional diffusion coefficient. The problems of more refined quantitative computations from the renormalized kinetic equation are severe, and furher study is necessary.