State-of-the-art models of massive black hole formation postulate that quasars at z > 6 reside in extreme peaks of the cosmic density structure in the early universe . Even so , direct observational evidence of these overdensities is elusive , especially on large scales ( \gg 1 Mpc ) as the spectroscopic follow-up of z > 6 galaxies is observationally expensive . Here we present Keck / DEIMOS optical and IRAM / NOEMA millimeter spectroscopy of a z \sim 6 Lyman-break galaxy candidate originally discovered via broadband selection , at a projected separation of 4.65 physical Mpc ( 13.94 arcmin ) from the luminous z =6.308 quasar J1030+0524 . This well-studied field presents the strongest indication to date of a large-scale overdensity around a z > 6 quasar . The Keck observations suggest a z \sim 6.3 dropout identification of the galaxy . The NOEMA 1.2mm spectrum shows a 3.5 \sigma line that , if interpreted as [ C ii ] , would place the galaxy at z =6.318 ( i.e. , at a line-of-sight separation of 3.9 comoving Mpc assuming that relative proper motion is negligible ) . The measured [ C ii ] luminosity is 3 \times 10 ^ { 8 } L _ { \odot } , in line with expectations for a galaxy with a star formation rate \sim 15 M _ { \odot } yr ^ { -1 } , as inferred from the rest-frame UV photometry . Our combined observations place the galaxy at the same redshift as the quasar , thus strengthening the overdensity scenario for this z > 6 quasar . This pilot experiment demonstrates the power of millimeter-wavelength observations in the characterization of the environment of early quasars .