  We present measurements of the clustering properties of bright ($L>L_{*}$)
z$\sim$4 Lyman Break Galaxies (LBGs) selected from the Oxford-Dartmouth Thirty
Degree Survey (ODT). We describe techniques used to select and evaluate our
candidates and calculate the angular correlation function which we find best
fitted by a power law, $\omega(\theta)=A_{w}\theta^{-\beta}$ with $A_{w}=15.4$
(with $\theta$ in arcseconds), using a constrained slope of $\beta=0.8$. Using
a redshift distribution consistent with photometric models, we deproject this
correlation function and find a comoving $r_{0}=11.4_{-1.9}^{+1.7}$
h$_{100}^{-1}$ Mpc in a $\Omega_m=0.3$ flat $\Lambda$ cosmology for
$i_{AB}\leq24.5$. This corresponds to a linear bias value of
$b=8.1_{-2.6}^{+2.0}$ (assuming $\sigma_{8}=0.9$). These data show a
significantly larger $r_{0}$ and $b$ than previous studies at $z\sim4$. We
interpret this as evidence that the brightest LBGs have a larger bias than
fainter ones, indicating a strong luminosity dependence for the measured bias
of an LBG sample. Comparing this against recent results in the literature at
fainter (sub-$L_{*}$) limiting magnitudes, and with simple models describing
the relationship between LBGs and dark matter haloes, we discuss the
implications on the implied environments and nature of LBGs. It seems that the
brightest LBGs (in contrast with the majority sub-$L_{*}$ population), have
clustering properties, and host dark matter halo masses, that are consistent
with them being progenitors of the most massive galaxies today.
