GRANULAR materials show both fluid-like and solid-like behaviour. Under weak shear they deform plastically; under high shear they flow. These materials exhibit other unusual kinds of behaviour, including segregation(1), density waves(2), convection(3) and anomalous sound propagation(4). Their dynamical properties are important in many industrial applications(5-7), In particular, the shaking of granular materials is used to mix, segregate and transport them. Vertically shaken granular materials undergo a transition to a convective state(6-14). Here we describe experiments which show that such convective motion can involve bubbling-the formation and upward motion of voids. The presence of gas between the grains is essential for bubbling to occur, and the instability shows characteristics of a Hopf bifurcation such as is seen at the onset of chaos. This bubbling behaviour may be analogous to that observed in fluidized beds(15,16), and might be expected to occur when soils are fluidized during earthquakes.