  We present in detail a calculation of the next-to-leading order QCD
corrections to the process $e^+e^-\to 3$ jets with massive quarks. To isolate
the soft and collinear divergencies of the four parton matrix elements, we
modify the phase space slicing method to account for masses. Our computation
allows for the prediction of oriented three jet events involving heavy quarks,
both on and off the Z resonance, and of any event shape variable which is
dominated by three jet configurations. We show next-to-leading order results
for the three jet fraction, the differential two jet rate, and for the thrust
distribution at various c.m. energies.
