Neoclassical bootstrap current is expected to provide a significant fraction of the equilibrium plasma current in tokamak reactors. Here we report a novel mechanism through which a bootstrap current may be driven even in a collisionless plasma. In analogy with the neoclassical mechanism, in which the collisional equilibrium established between trapped and passing electrons produces a steady state current, we show that resonant scattering of electrons by drift wave microturbulence provides an additional means of determining the equilibrium between trapped and passing electrons and thus driving a bootstrap current. Employing a linearized Fokker-Planck collision operator, the plasma current in the presence of both collisions and resonant electron scattering is computed, allowing for the relative strength of these two mechanisms to be quantified as a function of collisionality and fluctuation amplitude.