Clustering of galaxies at z=3 around the probable Damped Ly-alpha absorber towards QSO APM 08279+5255

[Abridged] We present results on the clustering og Lyman break galaxies (LBGs) around a probable damped Ly-alpha absorption (DLA) line cloud at z_DLA=2.974 from deep UBVI images of the field containing the quasar APM 08279+5255 (z=3.91). The large area covered by our images, 0.31 deg^2 or 40x40 Mpc co-moving at z=3, and their depth (27.6 mag arcsec^{-2}), allow us to identify 450 LBG candidates brighter than I(AB)=24.80 at 2.75<z<3.25. LBG candidates were selected using photometric redshift techniques that include priors within a redshift slice of width Wz=0.15 centered at z_DLA. Within that redshift slice, we find an enhancement of galaxies near the DLA using both the surface density and an estimator of the 3-D spatial over-density. The surface overdensity (3\times) is significant at the >95% significance level on scales 2.5<r<5 Mpc co-moving and imply that some DLA could reside in high density regions.