We present the analysis of a sub-damped Lyman-α system with neutral hydrogen column density, log N(H 0 ) (cm −2 ) = 20.0 ± 0.15 at z abs = 2.69 toward SDSS J123714.60+064759.5 (z em = 2.78). Using the VLT/UVES and X-shooter spectrographs, we detect H 2 , HD, and CO molecules in absorption with log N(H 2 , HD, CO) (cm −2 ) = 19.21 +0.13 −0.12 , 14.48 ± 0.05 and 14.17 ± 0.09 respectively. The overall metallicity of the system is super-solar ([Zn/H] = +0.34 relative to solar) and iron is highly depleted ([Fe/Zn] = −1.39), revealing metal-rich and dusty gas. Three H 2 velocity components spanning ∼125 km s −1 are detected. The strongest H 2 component, at z abs = 2.68955, with log N(H 2 ) = 19.20, does not coincide with the centre of the H i absorption. This implies that the molecular fraction in this component, f H 2 = 2N(H 2 )/(2N(H 2 )+N(H 0 )), is higher than the mean molecular fraction f H 2 = 1/4 in the system. We also found the Cl 0 associated with this H 2 component to have N(Cl 0 )/N(Cl + ) > 0.4, which points in the same direction. Cl 0 is tied to H 2 by charge exchange reactions, this means that the molecular fraction in this component is not far from unity. The kinetic temperature derived from the J = 0 and 1 rotational levels of H 2 is T = 108 +84 −33 K and the particle density derived from the C 0 ground-state fine structure level populations is n H0 ∼ 50-60 cm −3 . We derive an electronic density <2 cm −3 for a UV field similar to the Galactic one and show that the carbon-to-sulphur ratio in the cloud is close to the solar ratio. The size of the molecular cloud is probably smaller than 1 pc. Both the CO/H 2 = 10 −5 and CO/C 0 ∼ 1 ratios for f H 2 > 0.24 indicate that the cloud classifies as translucent, i.e., a regime where carbon is found both in atomic and molecular form. The corresponding extinction, A V = 0.14, albeit lower than the definition of a translucent sightline (based on extinction properties), is high for the observed H 0 column density. This means that intervening clouds with similar local properties but with higher column densities (i.e. larger physical extent) could be missed by current magnitudelimited QSO surveys. The excitation of CO is dominated by radiative interaction with the cosmic microwave background radiation (CMBR) and we derive T ex (CO) = 10.5 +0.8 −0.6 K when T CMBR (z = 2.69) = 10.05 K is expected. We measure N(HD)/2N(H 2 ) = 10 −5 . This is about 10 times higher than what is measured in the Galactic ISM for f H 2 = 1/4 but similar to what is measured in the Galactic ISM for higher molecular fractions. The astration factor of deuterium with respect to the primordial D/H ratio is only about 3. This can be the consequence of accretion of unprocessed gas from the intergalactic medium onto the associated galaxy. In the future, it will be possible to search efficiently for molecular-rich DLAs/sub-DLAs with X-shooter, but detailed studies of the physical state of the gas will still need UVES observations.