We create an ultracold neutral plasma by photoionization
of laser-cooled xenon atoms. The charge carrier density is as
high as 2 x10^{9} cm^{-3}, and the temperatures of electrons
and ions are as low as 100 mK and 10 uK, respectively. Such low
temperatures are unprecedented in neutral plasma physics. Plasma
behavior is evident in the trapping of electrons by the positive
ion cloud when the Debye screening length becomes smaller than
the size of the sample. We produce strongly coupled plasmas with
parameters such that the kinetic energy is small compared to
the Coulomb interaction energy between nearest neighbors. This
is the reverse of the usual situation for classical Debye plasmas.
Plasma oscillations are observed and serve as a probe of the electron
density distribution.