We present spectroscopic observations obtained with the FORS1 instrument on the ESO VLT under good seeing conditions of the radio-quiet z_em = 3.04 quasar Q1205-30 and its associated extended Lyα emission. The extended Lyα emission was originally found in a deep narrow band image targeting a z_abs ≈ Z_em Lyman-limit system in the spectrum of the QSO. Using spectral point-spread function fitting to subtract the QSO spectrum, we clearly detect the extended Lyα emission as well as two foreground galaxies at small impact parameters (2.12 ± 0.04 and 2.77 ± 0.07 arcsec). The red shifts of the two foreground galaxies are found to be z = 0.4732 and z = 0.865, We determine the redshift and velocity profile for the extended Lyα emission, and analyzing the velocity offsets between eight QSO emission lines we refine the quasar redshift determination. We use the new redshifts to infer the geometry of the complex. We find that the extended Lyα emission is clearly associated with the quasar. A Lyα luminosity of 5.6 × 10⁴³ erg s^-1 places this extended emission at the high luminosity end of the few previous detections around radio-quiet quasars. The extended Lyα emission is best explained by hydrogen falling into the dark matter halo inhabited by the quasar.