Aims:We present multiwavelength (X-ray/optical/near-infrared/millimetre) observations of GRB 051022 between 2.5 h and 1.15 yr after the event. It is the most intense gamma-ray burst ( 10-4 erg cm-2) detected by HETE-2, with the exception of the nearby GRB 030329. Methods: Optical and near infrared observations did not detect the afterglow despite a strong afterglow at X-ray wavelengths. Millimetre observations at Plateau de Bure (PdB) detected a source and a flare, confirming the association of this event with a moderately bright (R = 21.5) galaxy. Results: Spectroscopic observations of this galaxy show strong [O II], Hβ and [O III] emission lines at a redshift of 0.809. The spectral energy distribution (SED) of the galaxy implies AV (rest frame) = 1.0 and a starburst occuring 25 Myr ago, during which the star-forming-rate reached 50 M&sun;/yr. In conjunction with the spatial extent ( 1'') it suggests a very luminous (MV = - 21.8) blue compact galaxy, for which we also find Z˜ Z_&sun;. The X-ray spectrum shows evidence of considerable absorption by neutral gas with NH, X-ray = 3.47+0.48-0.47 × 1022 cm-2 (rest frame). Absorption by dust in the host galaxy at z = 0.809 certainly cannot account for the non-detection of the optical afterglow, unless the dust-to-gas ratio is quite different than that seen in our Galaxy (i.e. large dust grains). Conclusions: It is likely that the afterglow of the dark GRB 051022 was extinguished along the line of sight by an obscured, dense star forming region in a molecular cloud within the parent host galaxy. This galaxy is different from most GRB hosts being brighter than L* by a factor of 3. We have also derived a {SFR} ˜ 50 M_&sun;/yr and predict that this host galaxy will be detected at sub-mm wavelengths. Based on observations taken with the 1.0 m telescope at ARIES, with the 2.0 m telescope at Hanle, with the 1.5 m Carlos Sánchez at Observatorio del Teide, with the 1.5 m telescope at Observatorio de Sierra Nevada, with the 3.5 m Telescope at the Spanish-German Calar Alto Observatory, with the 3.5 m Telescopio Nazionale Galileo, with the 4.2 m William Herschel telescope, at the Observatorio del Roque de los Muchachos in La Palma, and with the 6.0 m Bolshoi Azimuthal Telescope at the Special Astrophysical Observatory in Zelenchukskaya.