A new surface plasmon resonator, in the form of a metal cylinder shaped like a teardrop, is proposed and modeled using hypersingular integral equations. Illuminating the apex of the teardrop along its axis of symmetry with TM-polarised light excites equal-magnitude surface plasmons counter-propagating around its periphery. Interference of these counter-propagating surface plasmons leads to resonant modes having very sharp line-widths (~0.6 nm) and large quality factors (~3400). In water, a Au teardrop supports resonant modes having large bulk sensitivities (~1900 nm/RIU) and remarkably large figures-of-merit (~1700), about 1000 × larger than the figure-of-merit of, e.g., isolated Au nano-spheres. The scattering cross-section of the structure near resonant modes exhibits a Fano-like line-shape. The teardrop should find applications as a high-quality surface plasmon resonator or as a biosensing element.