  The lasing threshold is studied of a multi-mode chaotic cavity (linear size D
>> wavelength \lambda) coupled to the outside through a small hole (linear size
d << \lambda). For sufficiently weak absorption by the boundaries, the
statistical distribution of the threshold is wide, its mean value being much
less than the pumping rate needed to compensate the average loss. The average
number N_{nc} >> 1 of non-competing excited modes is proportional to the square
root of the pumping rate. We use the classical model of spatial hole burning to
account for mode competition and find a reduction in the average number of
excited modes to N =3^{1/3} N_{nc}^{2/3}.
