  We compute the statistics of thermal emission from systems in which the
radiation is scattered chaotically, by relating the photocount distribution to
the scattering matrix - whose statistical properties are known from
random-matrix theory. We find that the super-Poissonian noise is that of a
black body with a reduced number of degrees of freedom. The general theory is
applied to a disordered slab and to a chaotic cavity, and is extended to
include amplifying as well as absorbing systems. We predict an excess noise of
amplified spontaneous emission in a random laser below the laser threshold.
