Concentrated particulate suspensions, commonplace in the pharmaceutical, cosmetic and food industries, display intriguing rheology. In particular, the dramatic increase in viscosity with strain rate (shear thickening and jamming), which is often observed at high-volume fractions, is of practical and fundamental importance. Yet, manufacture of these products and their subsequent dispensing often involves flow geometries substantially different from that of simple shear flow experiments. In this study, we show that the elongation and breakage of a filament of a colloidal fluid under tensile loading is closely related to the jamming transition seen in its shear rheology. However, the modified flow geometry reveals important additional effects. Using a model system with nearly hard-core interactions, we provide evidence of surprisingly strong viscoelasticity in such a colloidal fluid under tension. With high-speed photography, we also directly observe dilatancy and granulation effects, which lead to fracture above a critical elongation rate.