We report the discovery of the carbon-rich ultra metal-poor unevolved star J0815+4729. This dwarf star was selected from SDSS/BOSS as a metal-poor candidate and follow-up spectroscopic observations at medium-resolution were obtained with ISIS at William Herschel Telescope and OSIRIS at Gran Telescopio de Canarias. We use the FERRE code to derive the main stellar parameters, Teff=6215+-82 K, and logg=4.7+-0.5, an upper limit to the metallicity of [Fe/H]<~-5.8, and a carbon abundance of [C/Fe]>~+5.0, while [alpha/Fe]=0.4 is assumed. The metallicity upper limit is based on the Ca II K line, that at the resolving power of the OSIRIS spectrograph cannot be resolved from possible interstellar calcium. The star could be the most iron-poor unevolved star known, and is also amongst the ones with the largest overabundances of carbon. High-resolution spectroscopy of J0815+4729 will certainly help to derive other important element abundances, possibly providing new fundamental constraints on the early stages of the Universe, the formation of the first stars and the properties of the first supernovae.