  We report the measurement of the three-point correlation function (3PCF) of
galaxies for the Las Campanas Redshift Survey (LCRS). We have not only measured
the 3PCF in redshift space but also developed a method to measure the projected
3PCF which has simple relations to the real space 3PCF. Both quantities have
been measured as a function of triangle size and shape with only a fractional
uncertainty in each individual bin. Various tests derived from mock catalogs
have been carried out to assure that the measurement is stable and that the
errors are estimated reliably. Our results indicate that the 3PCFs both in
redshift space and in real space have small but significant deviations from the
well-known hierarchical form. The 3PCF in redshift space can be fitted by
$\Qsu=0.5\cdot 10^{[0.2+0.1({s\over s+1})^2]v^2}$ for $0.8<s_{12}<8 \mpc$ and
$s_{31}<16\mpc$, and the projected 3PCF by $\Qrpu=0.7r_p^{-0.3}$ for
$0.2<r_{p12}<3\mpc$ and $r_{p31}<6\mpc$ ($s$ and $r_p$ are in unit of $\mpc$),
though a systematic weak increase of $\Qrpu$ with $v$ at $r_p>1\mpc$ is noted.
The real-space $\Qru$ for $0.2 \ls r_{12} \ls 3\mpc$ and $r_{31}\ls 6\mpc$ can
be well described by half the mean 3PCF predicted by a CDM model with $\Omega_0
h=0.2$. Implications for the CDM cosmogonic models are discussed in detail with
the help of mock simulation samples.
