  ``Top--down'' models explain the observation of ultra high energy cosmic rays
(UHECR; $E \gsim 5 \cdot 10^{19}$ eV) through the decay of very massive,
long--lived ``$X$ particles''. If superparticles with masses near a TeV exist,
$X$ decays also lead to a significant flux of very energetic neutralinos,
assumed to be the (stable or long--lived) lightest superparticles. There is a
range of energies where neutrinos get absorbed in the Earth, but neutralinos
can still traverse it. These neutralinos could in principle be detected. We
calculate the detection rate in planned experiments such as OWL and EUSO. For
bino--like neutralinos, which have been considered previously, we find
detection rates below 1 event per Teraton of target and year in all cases;
often the rates are much smaller. In contrast, if the neutralino is
higgsino--like, more than ten events per year per Teraton might be observed, if
the mass of the $X$ particle is near its lower bound of $\sim 10^{12}$ GeV.
