  We have measured the angular correlation function w(theta) for a sample of
871 Lyman-break galaxies (LBGs) at z=3. Fitting a power-law to a weighted
average of w(theta) from 5 fields, we find the amplitude to be A_w=2
arcsec^{\beta} and the slope \beta=0.9. The slope is the same as in the local
and moderate redshift universe. A slope \beta=0.25 or shallower is ruled out by
the data at the 99.9% confidence level. Because N(z) of LBGs is well determined
from 376 spectroscopic redshifts, the real-space correlation function can be
derived from the angular one through the Limber transform. This inversion is
rather insensitive to the still relatively large errors on A_w and \beta, and
the spatial correlation length is much more tightly constrained than either of
these parameters. We estimate r_0=3.3 -0.6 +0.7 (2.1 -0.5 +0.4) h^{-1} Mpc
(comoving) for q_0=0.1 (0.5) at z=3.04 (h is in units of 100 km/s/Mpc). The
correlation length of LBGs at z=3 is comparable to that of present-day spiral
galaxies and is only about 50% smaller than that of the ellipticals; it is as
large or larger than any measured in galaxy samples at 0.3<z<1. By comparing
the observed galaxy correlation length to that of the mass predicted from CDM
theory, we estimate a bias for LBGs of b\sim 1.5 (4.5) for q_0=0.1 (0.5), in
agreement with our previous estimates based on preliminary spectroscopy. The
strong clustering and the large bias of the LBGs are consistent with biased
galaxy formation theories and provide additional evidence that these systems
are associated with massive dark matter halos. The clustering of LBGs at z=3
emphasizes that apparent evolution of galaxy clustering may be due as much to
variations in effective bias parameter among different samples as to evolution
in the mass distribution through gravitational instability.
