Fire whirls are powerful, spinning disasters for people and surroundings when they occur in large urban and wildland fires. Whereas fire whirls have been studied for fire-safety applications, previous research has yet to harness their potential burning efficiency for enhanced combustion. This article presents laboratory studies of fire whirls initiated as pool fires, but where the fuel sits on a water surface, suggesting the idea of exploiting the high efficiency of fire whirls for oil-spill remediation. We show the transition from a pool fire, to a fire whirl, and then to a previously unobserved state, a "blue whirl." A blue whirl is smaller, very stable, and burns completely blue as a hydrocarbon flame, indicating soot-free burning. The combination of fast mixing, intense swirl, and the water-surface boundary creates the conditions leading to nearly soot-free combustion. With the worldwide need to reduce emissions from both wanted and unwanted combustion, discovery of this state points to possible new pathways for reduced-emission combustion and fuel-spill cleanup. Because current methods to generate a stable vortex are difficult, we also propose that the blue whirl may serve as a research platform for fundamental studies of vortices and vortex breakdown in fluid mechanics.