We develop a topological model of ball lightning which explains its stability by the coupling of an air ball to a magnetic knot, a magnetic field with linked magnetic lines. Assuming that currents flow inside the ball, along short-circuited linked streamers following the lines of ∇¿B, the lifetime, energy, and radiated power of the average ball are correctly accounted for. The model explains why some witnesses do not feel heat, while others are burnt, and why filaments are seen to trail the ball in some cases. ¿ 1998 American Geophysical Union