Early JWST observations have uncovered a population of red sources that might represent a previously overlooked phase of supermassive black hole growth^1-3. One of the most intriguing examples is an extremely red, point-like object that was found to be triply imaged by the strong lensing cluster Abell 2744 (ref. ^4). Here we present deep JWST/NIRSpec observations of this object, Abell2744-QSO1. The spectroscopy confirms that the three images are of the same object, and that it is a highly reddened (A_V ≃ 3) broad emission line active galactic nucleus at a redshift of z_spec = 7.0451 ± 0.0005. From the width of Hβ (full width at half-maximum = 2,800 ± 250 km s^-1), we derive a black hole mass of M_BH=4_-1^+2×1 0^7M_⊙ . We infer a very high ratio of black-hole-to-galaxy mass of at least 3%, an order of magnitude more than that seen in local galaxies^5 and possibly as high as 100%. The lack of strong metal lines in the spectrum together with the high bolometric luminosity (L_bol = (1.1 ± 0.3) × 10^45 erg s^-1) indicate that we are seeing the black hole in a phase of rapid growth, accreting at 30% of the Eddington limit. The rapid growth and high black-hole-to-galaxy mass ratio of Abell2744-QSO1 suggest that it may represent the missing link between black hole seeds^6 and one of the first luminous quasars^7.