Context: The pioneer space mission for photometric planet searches, CoRoT, steadily monitors about 12 000 stars in each of its fields of view. Transit candidates can be detected early in the processing of the data and before the end of a run of observation. Aims: We report the detection of the first planet discovered by CoRoT and characterizing it with the help of follow-up observations. Methods: Raw data were filtered from outliers and residuals at the orbital period of the satellite. The orbital parameters and the radius of the planet were estimated by best fitting the phase folded light curve with 34 successive transits. Doppler measurements with the SOPHIE spectrograph permitted us to secure the detection against binaries and to estimate the mass of the planet. Results: The accuracy of the data is very high with a dispersion in the 2.17 min binned phase-folded light curve that does not exceed ~3.×10-4 in flux unit. The planet orbits a mildly metal-poor G0V star of magnitude V=13.6 in 1.5 days. The estimated mass and radius of the star are 0.95±0.15 M&sun; and 1.11±0.05 R&sun;. We find the planet has a radius of 1.49±0.08 R_Jup, a mass of 1.03±0.12 M_Jup, and a particularly low mean density of 0.38±0.05 g cm-3. The CoRoT space mission, launched on Dec. 27th, 2006, was developed and is operated by the CNES, with participation of the Science Program of ESA, ESTEC/RSSD, Austria, Belgium, Brazil, Germany and Spain. Based in part on observations with the SOPHIE spectrograph at Obs. de Haute Provence, France. Table [see full text] is only available in electronic form at http://www.aanda.org Individual photometric measurements are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/482/L17