We study the folding kinetics of a three-helix bundle protein using a coarse polymer model. The folding dynamics can be accurately represented by one-dimensional diffusion along a reaction coordinate selected to capture the transition state. By varying the solvent friction, we show that position-dependent diffusion coefficients are determined by microscopic transitions on a rough energy landscape. A maximum in the folding rate at intermediate friction is explained by "Kramers turnover" in these microscopic dynamics that modulates the rate via the diffusion coefficient; overall folding remains diffusive even close to zero friction. For water friction, we find that the "attempt frequency" (or "speed limit") in a Kramers model of folding is about 2 micros-1, with an activation barrier of about 2kBT, and a folding transition path duration of approximately equal to 100 ns, 2 orders of magnitude less than the folding time of approximately equal to 10 micros.