  We consider the production of neutralino pairs $\tchi^0_i\tchi^0_j$ at a high
energy hadron collider, putting a special emphasis on the case where one of
them is the lightest neutralino $\tchi^0_1$, possibly constituting the main
Dark Matter component. At tree level, the only relevant subprocess is $q\bar
q\to \tchi^0_i\tchi^0_j$, while the subprocess $gg\to \tchi^0_i\tchi^0_j$ first
appears at the one loop level. Explicit expressions for the $q\bar q$-helicity
amplitudes are presented, including the tree level contributions and the
leading-log one loop radiative corrections. For the one-loop $ gg\to
\tchi^0_i\tchi^0_j$ process, a numerical code named PLATONggnn is released,
allowing the computation of $d\sigma /d \that$ in any MSSM model with real soft
breaking parameters. It turns out that acceptable MSSM benchmark models exist
for which the $q\bar q $ and the gluonic contributions may give comparable
effects at LHC, due to the enhanced gluonic structure functions at low
fractional momenta. Depending on the values of the MSSM parameters, we find
that the LHC neutralino pair production may provide sensitive tests of SUSY
models generating neutralino Dark Matter.
