  We evaluate the rare radiative kaon decays K_{L,S} -> 3 gamma. Applying the
requirements of gauge invariance and Bose symmetry, we derive a general form of
the decay amplitude, including both parity-conserving and parity-violating
contributions. We employ a chiral-Lagrangian approach combined with dimensional
analysis arguments to estimate the branching ratios of these decays in the
standard model, obtaining values as large as B(K_L -> 3 gamma) ~ 1 x 10^{-14}
and B(K_S -> 3 gamma) ~ 2 x 10^{-17}, which exceed those found previously by a
few orders of magnitude. Measurements on the branching ratios which are
significantly larger than these numbers would likely hint at the presence of
new physics beyond the standard model.
