We present the initial imaging and spectroscopic data acquired as part of the Very Large Telescope (VLT) VIMOS Lyman-break galaxy Survey. UBR (or UBVI) imaging covers five ≈36 × 36 arcmin² fields centred on bright z > 3 quasi-stellar objects (QSOs), allowing ≈21 000 2 < z < 3.5 galaxy candidates to be selected using the Lyman-break technique. We performed spectroscopic follow-up using VLT VIMOS, measuring redshifts for 1020 z > 2 Lyman-break galaxies and 10 z > 2 QSOs from a total of 19 VIMOS pointings. From the galaxy spectra, we observe a 625 ± 510 km s^-1 velocity offset between the interstellar absorption and Lyman α emission-line redshifts, consistent with previous results. Using the photometric and spectroscopic catalogues, we have analysed the galaxy clustering at z≈ 3. The angular correlation function, w(θ), is well fitted by a double power law with clustering scalelength, r₀= 3.19^+0.32_-0.54 h^-1 Mpc and slope γ= 2.45 for r < 1 h^-1 Mpc and r₀= 4.37^+0.43_-0.55 h^-1 Mpc with γ= 1.61 ± 0.15 at larger scales. Using the redshift sample we estimate the semiprojected correlation function, w_p(σ), and, for a γ= 1.8 power law, find r₀= 3.67^+0.23_-0.24 h^-1 Mpc for the VLT sample and r₀= 3.98^+0.14_-0.15 h^-1 Mpc for a combined VLT+Keck sample. From ξ(s) and ξ(σ, π), and assuming the above ξ(r) models, we find that the combined VLT and Keck surveys require a galaxy pairwise velocity dispersion of ≈700 km s^-1, higher than ≈400 km s^-1 assumed by previous authors. We also measure a value for the gravitational growth rate parameter of β(z= 3) = 0.48 ± 0.17, again higher than that previously found and implying a low value for the bias of b= 2.06^+1.1_-0.5. This value is consistent with the galaxy clustering amplitude which gives b= 2.22 ± 0.16, assuming the standard cosmology, implying that the evolution of the gravitational growth rate is also consistent with Einstein gravity. Finally, we have compared our Lyman-break galaxy clustering amplitudes with lower redshift measurements and find that the clustering strength is not inconsistent with that of low-redshift L* spirals for simple 'long-lived' galaxy models. Based on data obtained with the National Optical Astronomy Observatories (NOAO) Mayall 4-m Telescope at Kitt Peak National Observatory, USA (programme ID: 06A-0133), the NOAO Blanco 4-m Telescope at Cerro Tololo Inter-American Observatory, Chile (programme IDs: 03B-0162 and 04B-0022) and the European Southern Observatory (ESO) Very Large Telescope (VLT), Chile (programme IDs: 075.A-0683, 077.A-0612 and 079.A-0442).