Parallel thermal conduction along stochastic magnetic field lines may be re
duced because the heat-conducting electrons become trapped and detrapped be
tween regions of strong magnetic field (magnetic mirrors). The problem redu
ces to a simple but realistic model for diffusion of monoenergetic electron
s based on the fact that when there is a reduction of diffusion, it is cont
rolled by a subset of the mirrors, the principal mirrors. The diffusion red
uction can be considered as equivalent to an enhancement of the pitch angle
scattering rate. Therefore, in deriving the collision integral, we modify
the pitch angle scattering term. We take into account the full perturbed el
ectron-electron collision integral, as well as the electron-proton collisio
n term. Finally, we obtain the four plasma transport coefficients and the e
ffective thermal conductivity. We express them as reductions from the class
ical values. We present these reductions as functions of the ratio of the m
agnetic field decorrelation length to the electron mean free path at the th
ermal speed V-T = (2kT/m(e))(1/2). We briefly discuss an application of our
results to clusters of galaxies.