We present results on the clustering of Lyman break galaxies (LBGs) around a probable damped Lyα absorption line cloud (DLA) at zabs = 2.974 from deep UBVI images of the field containing the quasar APM 08279+5255 (zem = 3.91). The large area covered by our images, 0.31 deg2 or ~40 × 40 Mpc comoving at redshift z = 3, and their depth, μI,AB(sky) 27.6 mag arcsec-2, allow us to identify ~450 LBG candidates brighter than IAB = 24.80 at 2.75 z 3.25 both close (50 kpc) to the DLA line of sight and up to 20 Mpc (comoving) from the DLA, i.e., physically unrelated. LBG candidates were identified using photometric redshift techniques that include the I magnitude as a prior estimate in addition to the colors. The two are combined using Bayes's theorem. This helps to break the degeneracies that occur in a pure spectral template fitting scheme. The overall rms is σz 0.15 at z ~ 3 based on our analysis of photometric redshifts in the HDF-N. From the redshift likelihood distributions, we selected LBG galaxies within a redshift slice of width Wz = 0.15( σz) centered on the redshift of the DLA zabs. Within that redshift slice, we find an enhancement of galaxies near the DLA using both the surface density (Σ/Σg 3) and an estimator of the three-dimensional spatial overdensity (n/g ~ 5 ± 3). The surface overdensity Σ/Σg is significant at the more than 95% significance level on scales 2.5 rθ 5 Mpc comoving. The overdensity cannot be related to the QSO environment since the QSO is at zem = 3.91. These results imply that some DLA could reside in high-density regions. We search within 45'' from the line of sight for galaxies responsible for the DLA and find one candidate with zphot = 3.03 that is 26'' (145 kpc physical) away. From its magnitude I = 24.65 ± 0.2, its luminosity is MI,AB = -21.35. Due to its large impact parameter, however, this galaxy is not a likely candidate for the absorber.
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