  We study the statistics of charge transport in a chaotic cavity attached to
external reservoirs by two openings of different size which transmit non-equal
number of quantum channels. An exact formula for the cumulant generating
function has been derived by means of the Keldysh-Green function technique
within the circuit theory of mesoscopic transport. The derived formula
determines the full counting statistics of charge transport, i.e., the
probability distribution and all-order cumulants of current noise. It is found
that, for asymmetric cavities, in contrast to other mesoscopic systems, the
third-order cumulant changes the sign at high biases. This effect is attributed
to the skewness of the distribution of transmission eigenvalues with respect to
forward/backward scattering. For a symmetric cavity we find that the third
cumulant approaches a voltage-independent constant proportional to the
temperature and the number of quantum channels in the leads.
