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[en] In the standard picture of structure formation, the first massive galaxies are expected to form at the highest peaks of the density field, which constitute the cores of massive proto-clusters. Luminous quasars (QSOs) at z ∼ 4 are the most strongly clustered population known, and should thus reside in massive dark matter halos surrounded by large overdensities of galaxies, implying a strong QSO–galaxy cross-correlation function. We observed six z ∼ 4 QSO fields with VLT/FORS, exploiting a novel set of narrow-band filters custom designed to select Lyman Break Galaxies (LBGs) in a thin redshift slice of , mitigating the projection effects that have limited the sensitivity of previous searches for galaxies around QSOs. We find that LBGs are strongly clustered around QSOs, and present the first measurement of the QSO–LBG cross-correlation function at z ∼ 4, on scales of (comoving). Assuming a power-law form for the cross-correlation function , we measure for a fixed slope of . This result is in agreement with the expected cross-correlation length deduced from measurements of the QSO and LBG auto-correlation function, and assuming a deterministic bias model. We also measure a strong auto-correlation of LBGs in our QSO fields, finding for a fixed slope of , which is ∼4 times larger than the LBG auto-correlation length in blank fields, providing further evidence that QSOs reside in overdensities of LBGs. Our results qualitatively support a picture where luminous QSOs inhabit exceptionally massive () dark matter halos at z ∼ 4.