We report the results of a search for a charged Higgs boson in the decays of top quarks produced in pp collisions at a center-of-mass energy of 1.96 TeV. We use a data sample corresponding to an integrated luminosity of 193  pb−1 collected by the upgraded Collider Detector at Fermilab. No evidence for charged Higgs production is found, allowing 95% C.L. upper limits to be placed on BR(t→H+b) for different charged Higgs decay scenarios. In addition, we present in the minimal supersymmetric standard model (mH±,tanβ) plane the first exclusion regions with radiative and Yukawa coupling corrections.