We present results on the clustering of Lyman break galaxies (LBGs) around a probable damped Lyalpha absorption line cloud (DLA) at z(abs) = 2.974 from deep UBVI images of the field containing the quasar APM 08279+ 5255 (z(em) = 3.91). The large area covered by our images, 0.31 deg(2) or similar to 40 x 40 Mpc comoving at redshift z = 3, and their depth, mu(I,A,B) (sky) similar or equal to 27.6 mag arcsec(-2), allow us to identify similar to450 LBG candidates brighter than I-AB = 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 sigma(z) similar or equal to 0.15 at z similar to 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 W-z = 0.15 (similar or equal to sigma(z)) centered on the redshift of the DLA z(abs). Within that redshift slice, we find an enhancement of galaxies near the DLA using both the surface density (Sigma/Sigma(g) approximate to 3) and an estimator of the three-dimensional spatial overdensity (n/(n) over bar (g) similar to 5 +/- 3). The surface overdensity Sigma/Sigma(g) is significant at the more than 95% significance level on scales 2.5 < r(θ) < 5 Mpc comoving. The overdensity cannot be related to the QSO environment since the QSO is at z(em) = 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 z(phot) = 3.03 that is 26" (145 kpc physical) away. From its magnitude I = 24.65 +/- 0.2, its luminosity is M-I,M-AB = - 21.35. Due to its large impact parameter, however, this galaxy is not a likely candidate for the absorber.