  The quest for structure indicators at earlier and earlier times in the
evolution of the universe has led to the search for objects with ever higher
redshifts. The Palomar Transit Grism Survey has produced a large sample of high
redshift quasars ($z>2.7$), allowing statistical analysis of correlation
between quasar positions. In this study, clustering is identified through
comparison with $100 000$ Monte Carlo generated, randomly populated volumes,
which are identical to the observed region in spatial coordinates, redshift
distribution, and number of quasars. Three pairs have been observed with
comoving separations of 11.34, 12.97, and 24.13 h_{50}^{-1}Mpc (assuming
$q_0=0.5$), smaller separations than would be expected to arise by chance in an
unclustered distribution. Selection effects are ruled out as a false source of
clustering by scrambling the observed quasar coordinates and redshifts, which
gives a pair separation distribution nearly identical to that of the Monte
Carlo distribution. Tests using the distribution of pair separations and
nearest neighbor distances show that the observed pairs have a probability less
than 0.1% of arising in an unclustered distribution. Using a maximum likelihood
technique to estimate the correlation length $r_0$, assuming $\xi(r) =
(r/r_0)^{-1.8}$, we find $r_0 = 35\pm15 h_{50}^{-1}Mpc$ (comoving, $q_0=0.5$,
1$\sigma$ errors), a value much larger than the correlation length of
present-day galaxies.
