We report on a case of conjoined twinning (CT) consistent with fusion of two embryos followed by resorption of the cranial half of one of them, resulting in a normal male baby with the lower half of a male parasitic twin fused to his chest. Fluorescent in situ hybridization (FISH) studies suggested that the parasitic twin was male, and DNA typing studies demonstrated dizygosity. Although incomplete fission is the usual explanation for conjoined twins, the unusual perpendicular orientation of the parasite to the autosite supports a mechanism observed in mares in which early fusion of two embryos is followed by resorption due to compromised embryonic polarity.