There are several types of instabilities in fluid mechanics that lead to spontaneous chaotic mixing and intricate patterns. Classical examples include the Kelvin-Helmholtz instability(1,2) in shear layers, the instability of Taylor-Couette flow between rotating cylinders(3,4) and the Rayleigh-Benard instability in thermal convection(5). More recently, a variety of two- and three-dimensional chaotic mixing phenomena have been observed in other geometries(6-9). Mixing in granular flows(10,11), unlike that in stirred fluids, is thought to be diffusive-although periodic forcing has been used to enhance granular mixing(12-13), spontaneous chaotic granular mixing has not previously been reported. Here we report the observation of chaotic granular mixing patterns in simple cylindrical tumblers partially filled with fine grains. The patterns form spontaneously when sufficiently fine grains (less than or similar to 300 mu m diameter) are blended. We identify the mechanism by which the chaotic patterns are produced: a periodic stick-slip behaviour occurs in the shear layer separating static and flowing regions of grains. This causes weakly cohesive grains to mix at rates overwhelmingly exceeding those achievable for previously studied(11,14) freely flowing grains.