We present 3 mm observations of the quasar J0015+1842 at z=2.63 with the NOrthern Extended Millimeter Array (NOEMA). Our data reveal molecular gas, traced with a Gaussian CO(3-2) line, with a remarkably high velocity dispersion (FWHM=1010 +/- 120 km s^-1) that corresponds to a total molecular mass MH2approximate to (3.4-17) x 10¹⁰ Mcircle dot, depending on the adopted CO-to-H2 conversion factor alpha CO=(0.8-4.0) Mcircle dot (km s^-1 pc²)^-1. Assuming the 3 mm continuum emission is thermal, we derive a dust mass of about Mdustsimilar to 5x10⁸ Mcircle dot. J0015+1842 is located in the molecular gas-rich region in the IR versus CO line luminosity diagram, in between the main locus of main-sequence and sub-millimetre galaxies and that of most other active galactic nuclei targeted so far for CO measurements. While the high velocity dispersion of the CO line suggests a merging system, J0015+1842 is observed to be a regular, only very moderately dust-reddened (AVsimilar to 0.3-0.4) type I quasar from its UV-optical spectrum, from which we infer a mass of the super-massive black hole of about MBHapproximate to 6x10⁸ Mcircle dot. We suggest that J0015+1842 is observed at a galaxy evolutionary stage where a massive merger has brought significant amounts of gas towards an actively accreting super-massive black hole (quasar). While the host still contains a large amount of dust and molecular gas with a high velocity dispersion, the quasar has already cleared the way towards the observer, likely through powerful outflows, as has recently been revealed by optical observations of the same object. High angular resolution observations of this and similar systems are expected to help us better determine the respective importance of evolution and orientation in the appearance of quasars and their host galaxies. These observations have the potential to investigate early feedback and star-formation processes in galaxies in their quasar phases.