Top quark production offers the unique opportunity to search for a charged Higgs boson (H±), as the contribution from t⃗ H+b⃗ τ+νb 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 eτ+ET+jets and μτ+ET+jets signatures to set an upper limit on the branching ratio of B(t⃗ H+b) in 106 pb-1 of data. The upper limit is in the range 0.5 to 0.6 at 95% C.L. for H+ masses in the range 60 to 160 GeV, assuming the branching ratio for H+→τν is 100%. The τ lepton is detected through its 1-prong and 3-prong hadronic decays.