  We present the first calculation of the kinetic Sunyaev-Zel'dovich (kSZ)
effect due to the inhomogeneous reionization of the universe based on detailed
large-scale radiative transfer simulations of reionization. The resulting sky
power spectra peak at l=2000-8000 with maximum values of
l^2C_l~1\times10^{-12}. The peak scale is determined by the typical size of the
ionized regions and roughly corresponds to the ionized bubble sizes observed in
our simulations, ~5-20 Mpc. The kSZ anisotropy signal from reionization
dominates the primary CMB signal above l=3000. This predicted kSZ signal at
arcminute scales is sufficiently strong to be detectable by upcoming
experiments, like the Atacama Cosmology Telescope and South Pole Telescope
which are expected to have ~1' resolution and ~muK sensitivity. The extended
and patchy nature of the reionization process results in a boost of the peak
signal in power by approximately one order of magnitude compared to a uniform
reionization scenario, while roughly tripling the signal compared with that
based upon the assumption of gradual but spatially uniform reionization. At
large scales the patchy kSZ signal depends largely on the ionizing source
efficiencies and the large-scale velocity fields: sources which produce photons
more efficiently yield correspondingly higher signals. The introduction of
sub-grid gas clumping in the radiative transfer simulations produces
significantly more power at small scales, and more non-Gaussian features, but
has little effect at large scales. The patchy nature of the reionization
process roughly doubles the total observed kSZ signal for l~3000-10^4 compared
to non-patchy scenarios with the same total electron-scattering optical depth.
