  The cosmic microwave background (CMB) radiation is characterized by
well-established scales, the 2.7 K temperature of the Planckian spectrum and
the $10^{-5}$ amplitude of the temperature anisotropy. These features were
instrumental in indicating the hot and equilibrium phases of the early history
of the Universe and its large scale isotropy, respectively. We now reveal one
more intrinsic scale in CMB properties. We introduce a method developed
originally by Kolmogorov, that quantifies a degree of randomness (chaos) in a
set of numbers, such as measurements of the CMB temperature in some region.
Considering CMB as a composition of random and regular signals, we solve the
inverse problem of recovering of their mutual fractions from the temperature
sky maps. Deriving the empirical Kolmogorov's function in the Wilkinson
Microwave Anisotropy Probe's maps, we obtain the fraction of the random signal
to be about 20 per cent, i.e. the cosmological sky is a weakly random one. The
paper is dedicated to the memory of Vladimir Arnold (1937-2010).
