Supermassive black holes (SMBHs) and their host galaxies are generally thought to coevolve, so that the SMBH achieves up to about 0.2 to 0.5% of the host galaxy mass in the present day. The radiation emitted from the growing SMBH is expected to affect star formation throughout the host galaxy. The relevance of this scenario at early cosmic epochs is not yet established. We present spectroscopic observations of a galaxy at redshift z = 3.328, which hosts an actively 1 accreting, extremely massive BH, in its final stages of growth. The SMBH mass is roughly one-tenth the mass of the entire host galaxy, suggesting that it has grown much more efficiently than the host, contrary to models of synchronized coevolution. The host galaxy is forming stars at an intense rate, despite the presence of a SMBH-driven gas outflow.Several lines of observational evidence, spanning a wide range of cosmic epochs, have led to a commonly accepted picture wherein supermassive black holes (SMBHs, M BH > 10 6 M ⊙ ; M ⊙ is the solar mass) coevolve with their host galaxies (1-4). Moreover, energy-and/or momentumdriven "feedback" from accreting SMBHs (Active Galactic Nuclei; AGN) is thought to quench star formation in the host galaxy (5). To directly test the relevance of such scenarios at early cosmic epochs (high redshifts, z) requires the most basic properties of SMBHs and their hosts, including masses and growth rates, to be observed. Several observational studies found that at z < ∼ 2 (more than 3.3 billion years after the Big Bang), the typical BH-to-stellar mass ratio, CID-947 is an x-ray-selected, unobscured AGN at z = 3.328, detected in both XMM-Newtonand Chandra x-ray imaging data of the COSMOS field [see Fig. S4 and sections S2 and S4 in the supplementary materials (16)]. We obtained a near-infrared (IR) K-band spectrum of CID-947 using the MOSFIRE instrument at the W. M. Keck telescope, which at z = 3.328 covers the hydrogen Hβ broad emission line (see details in section S1 in the supplementary materials).The calibrated spectrum shows a very broad Hβ emission line, among other features ( Fig. 1).Our spectral analysis indicates that the monochromatic AGN luminosity at rest-frame 5100Åis L 5100 = 3.58 By combining this line width with the observed L 5100 and relying on an empirically calibrated estimator for M BH , based on the virial motion of ionized gas near the SMBH (17), we obtain M BH = 6.9All the reported measurement-related uncertainties are derived by a series of simulations and represent the 16th and 84th quantiles of the resulting distributions.These simulations indicate a SMBH mass larger than 3.6 × 10 9 M ⊙ at the 99% confidence level (see sections S1.2 and S3 for more details). Determinations of M BH from single-epoch spectra of the Hβ emission line are known to also be affected by significant systematic uncertainties, of up to ∼ 0.3 to 0.4 dex. For a detailed discussion of some of the systematics and related issues, see §S3 in the supplementary materials. This high M BH is comparable with some of the most massive BHs...