We present results of a search for the top quark decaying to a 
charged Higgs boson ($H^+$) in $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV
at the Fermilab Tevatron.  Assuming that $H^+ \rightarrow\tau\nu_\tau$
is the dominant $H^+$ decay mode, we exclude regions of the 
($m_{H^+}$,m_t) plane for values of the branching ratio 
$B(H^+ \rightarrow\tau\nu_\tau)=0.5,0.75, and 1.0$.  We interpret
the results in terms of the parameter tan$\beta$ in the two-Higgs-doublet
model.