Abstract

Context. Understanding the relationship between the formation and evolution of galaxies and their central super-massive black holes (SMBH) is one of the main topics in extragalactic astrophysics. Links and feedback may reciprocally affect both black hole and galaxy growth. Aims. Observations of the CO line at the main epoch of galaxy and SMBH assembly (z = 2-4) are crucial to investigating the gas mass, star formation, and accretion onto SMBHs, and the effect of AGN feedback. Potential correlations between AGN and host galaxy properties can be highlighted by observing extreme objects. Methods. We targeted CO(3-2) in ULAS J1539+0557, a hyper-luminous quasar (L-bol > 10(48) erg/s) at z = 2.658, selected through its unusual red colour in the UKIDSS Large Area Survey (ULAS). Results. We find a molecular gas mass of 4.1 +/- 0.8 x 10(10) M-circle dot, by adopting a conversion factor alpha = 0.8 M-circle dot K-1 km s(-1) pc(2), and a gas fraction of similar to 0.4-0.1, depending mostly on the assumed source inclination. We also find a robust lower limit to the star-formation rate (SFR = 250-1600 M-circle dot/yr) and star-formation efficiency (SFE = 25-350 L-circle dot/(K kms(-1) pc(2)) by comparing the observed optical-near-infrared spectral energy distribution with AGN and galaxy templates. The black hole gas consumption timescale, M(H-2)/(M) over dot(acc), is similar to 160 Myr, similar to or higher than the gas consumption timescale. Conclusions. The gas content and the star formation efficiency are similar to those of other high-luminosity, highly obscured quasars, and at the lower end of the star-formation efficiency of unobscured quasars, in line with predictions from AGN-galaxy co-evolutionary scenarios. Further measurements of the (sub) mm continuum in this and similar sources are mandatory to obtain a robust observational picture of the AGN evolutionary sequence.