Deformation and breakup of a viscous drop in a Bingham liquid is investigated numerically with a volume-of-fluid scheme. Initially, a spherical drop is placed between two moving parallel plates. For our parameters, the matrix liquid has yielded. The competing effects driving the motion are the shear and interfacial tension. When interfacial tension effects dominate, the drop evolves to a steady shape which is elongated compared with the case when the outer liquid is Newtonian. Prior to breakup, stress levels are highest at the ends of the elongated drop. When shearing effects dominate, the drop breaks up, again with features that are elongated compared with the Newtonian counterpart. After the initial breakup, the daughter drops assume steady shapes.