Abstract: We study the quantum statistics of single-mode radiation emitted by an atomic ensemble when the ensemble is initially prepared in a superradiant Dicke state. We show that while the radiation is well approximated by the Glauber coherent state at early times in the evolution, the emission can be truly quantum at later times. In particular, one can observe a large amount of photon-number squeezing in the emission under certain conditions; even a Fock state can be produced. We discuss the quantum statistics of the emission for various parameters, including different initial conditions for the atomic ensemble. To obtain these results, we have developed a formalism where we are able to calculate the quantum statistics of the emission over long time-scales even when the number of atoms in the ensemble is quite large.