We present a model for the generation of the nonthermal electron distributions observed in interplanetary space and required in some solar wind acceleration and coronal heating theories. The particles are accelerated by fast mode waves generated by an unspecified mechanism (perhaps reconnection associated with microflares) in the upper chromosphere or lower transition region. The waves interact and cascade to higher wavenumbers where they eventually energize electrons out of an initially Maxwellian distribution. Coulomb collisions limit the number that are accelerated. As the electrons are driven to higher energy they more readily escape from the acceleration site. Escape limits the efficiency of the acceleration at high energies. The distributions do not extend into the ultrarelativistic regime like those generated under solar flare conditions, but do have significant nonthermal tails. ¿ 1998 American Geophysical Union