  The cross section for the reaction $e^+e^- \to t\bar{t} H$ depends
sensitively on the top quark Yukwawa coupling $\lambda_t$. We calculate the
rate for $t\bar{t}H$ production, followed by the decay $H\to b\bar{b}$, for a
Standard Model Higgs boson with 100 < m_H <130 GeV. We interface with ISAJET to
generate QCD radiation, hadronization and particle decays. We also calculate
the dominant $t\bar{t}b\bar{b}$ backgrounds from electroweak and QCD processes.
We consider both semileptonic and fully hadronic decays of the $t\bar{t}$
system. In our analysis, we attempt full reconstruction of the top quark and W
boson masses in the generated events. The invariant mass of the remaining
b-jets should show evidence of Higgs boson production. We estimate the accuracy
with which $\lambda_t$ can be measured at a linear e^+e^- collider. Our
results, including statistical but not systematic errors, show that the top
quark Yukawa coupling can be measured to 6-8 % accuracy with 1000 fb^{-1} at
$E_{CM}=1 TeV$, assuming 100 % efficiency for b-jet tagging. The accuracy of
the measurement drops to 17-22 % if only a 60 % efficiency for b-tagging is
achieved.
