We have studied the problem of strongly time-dependent, two-dimensional, incompressible, infinite Prandtl number thermal convection in an aspect-ratio five box for a non-Newtonian power-law rheology and a heated from below configuration, as applied to mantle dynamics. The convection equations are solved by means of a characteristics-based method with a Lagrangian formulation of the total derivative in the energy equation. Iterations are required at each time step for solving the nonlinear momentum equation. Bicubic splines are used for the spatial discretization. The transition from mildly time-dependent to the strongly chaotic or turbulent regime, in which the plumes become disconnected, occurs at much lower Nusselt numbers (Nu), between 20 and 25, than for Newtonian rheology. TheNuversus Rayleigh number(Ra)relationship displays a kink at this transition. Rising non-Newtonian plumes exhibit much greater curvature in their ascent than Newtonian ones and are strongly attracted by descending currents at the top. The viscosity field becomes strongly mixed and assumes a granular character in the turbulent regime. Horizontal spectral decomposition of the viscosity field outside the boundary layer shows that in the chaotic regime the fluctuations about the mean viscosity do not vary by more than an order of magnitude for one and a half decade in horizontal wavenumber. Vorticity fields produced by non-Newtonian convection are much more intense than Newtonian. Increasing the power law index sharpens the chaotic behavior of the flow with highRa.