Top quark production offers the unique opportunity to search for a charged Higgs boson (H{sup {+-}}), as the contribution from t{yields}H{sup +}b{yields}{tau}{sup +}{nu}b can be large in extensions of the standard model. We use results from a search for top quark pair production by the Collider Detector at Fermilab (CDF) in the e{tau}+Ee{sub T}+jets and {mu}{tau}+Ee{sub T}+jets signatures to set an upper limit on the branching ratio of B(t{yields}H{sup +}b) in 106 pb{sup -1} of data. The upper limit is in the range 0.5 to 0.6 at 95% C.L. for H{sup +} masses in the range 60 to 160 GeV, assuming the branching ratio for H{sup +}{yields}{tau}{nu} is 100%. The {tau} lepton is detected through its 1-prong and 3-prong hadronic decays. (c) 2000 The American Physical Society.