We present the results of a search in p¯p collisions at s=1.8 TeV for the top quark decaying to a charged Higgs boson (H±). We search for dilepton final states from the decay chain tt¯→HH (or HW, or WW) + bb¯→ll+X. In a sample of 19.3 pb−1 collected during 1992-93 with the Collider Detector at Fermilab, we observe 2 events with a background estimation of 3.0 ± 1.0 events. Limits at 95% C.L. in the (Mtop,MH±) plane are presented. For the case Mtop