The Standard Model predicts the existence of one neutral scalar Higgs boson, which is a remnant of the mechanism that breaks the SU(2)[sub L]xU(1)[sub Y] electroweak symmetry and generates masses for the heavy vector bosons and fermions. Many extensions to the Standard Model predict two or more Higgs doublets, resulting in a larger spectrum of Higgs bosons including a charged Higgs boson (H[sup [+-]]). For a light charged Higgs boson mass, the top decay into a charged Higgs boson and bottom quark might occur. This thesis presents results of a direct search for this top quark decay mode via the charged Higgs decay to a tau lepton and tau-neutrino, using the hadronic decays of the tau leptons. The search data consist of 100 pb[sup -1] of Run 1 data collected between 1992-1995 at the CDF detector, from p[anti p] collisions at a center-of-mass energy of 1.8 TeV produced at Fermilab's Tevatron accelerator. A total of seven events are observed in two search channels with an expected background contribution of 7.4[+-]2.0 events coming from fake taus (5.4[+-]1.5), heavy vector boson decays with jets (1.9[+-]1.3) and dibosons(0.08[+-]0.06). Lacking evidence for a signal, we set limits on charged Higgs production at the 95% confidence level in the charged Higgs mass plane versus tan[beta](a parameter of the theory) for a top quark mass of 175 GeV/c[sup 2] and for top production cross sections ([sigma][sub t[anti t]]) of 5.0 and 7.5 pb, assuming the Type-II Two-Higgs-Doublet-Model. For large tan[beta], this analysis excludes a charged Higgs boson of mass below 147(158)GeV/c[sup 2] for [sigma][sub t[anti t]]=5.0(7.5)pb. Using the Standard Model measured top quark cross section from CDF, this limit increases to 168 GeV/c[sup 2] and we also exclude a branching fraction of top decays via this charged Higgs mode of greater than 43% for charged Higgs masses below 168 GeV/c[sup 2].