We describe a general methodology for introducing thorough chaotic mixing in microdroplets. The mixing properties of fluid flows in microdroplets are governed by their symmetries, which give rise to invariant surfaces serving as barriers to transport. Complete three-dimensional mixing by chaotic advection requires destruction of all flow invariants. To illustrate this idea, we demonstrate that complete mixing can be obtained in a time-dependent flow produced by moving a microdroplet along a two-dimensional path. The theoretical predictions are confirmed by experiments that use the thermocapillary effect to manipulate microdroplets.