Correlations between antiprotons have been studied in approximately 3.9 
million hadronic Z$^0$ decays recorded with the OPAL detector at LEP 
between 1992-1995.  Antiprotons were identified in the central tracking 
chamber using their specific energy loss in the drift chamber gas.  
The correlations were studied as a function of $Q$, the 4-momentum difference 
of the pair.  A deficiency of pairs in the region $Q<3$~GeV was observed, 
which can be attributed to Fermi-Dirac statistics.   The parameters of the 
Fermi-Dirac correlation were measured to be 
$ \lambda = 0.76 \pm 0.16 {\mathrm {(stat)}} 
\pm 0.29 {\mathrm {(syst)}}$ for the strength and 
$ R = 0.142 \pm 0.035 {\mathrm {(stat)}} \pm 0.047 {\mathrm {(syst)}}$~fm 
for the antiproton source radius.  In order to establish 
that this effect is due to the identical nature of the particles, we also 
studied antiproton-$\overline{\Lambda}$ correlations and did not observe a 
similar effect.