Compound drops arise from the contact of three immiscible fluids and can assume various geometric forms based on the interfacial chemistry of the phases involved. Here we present a study of a new class of compound drops that is sessile on a solid surface. The possible geometries are demonstrated experimentally with appropriate fluid combinations and accounted for with a quantitative theoretical description. Although such systems are broadly controlled by relative interfacial energies, subtleties such as the van der Waals force and effects of micro-gravity, despite drop sizes being well below the capillary length, come into play in determining the equilibrium state that is achieved. The drying of a compound sessile drop was measured experimentally, and the process revealed a novel transition between different characteristic configurations of compound sessile drops. Such drops may prove to be useful as the first step towards development of functional surfaces in applications such as soft optics, photonics and surface encapsulation.