Extremely faint galaxies (mu_V>27 mag/arcsec^2), have only been discovered in the Local Group. These galaxies are very low in mass (tens of 10^5 Msun) and compact (effective radius <1 kpc). These objects populate the least massive dark matter haloes capable of producing stars, providing us with valuable insights into the nature of star formation at such low masses. Here we report the serendipitous discovery of Nube; an extremely faint galaxy (central surface brightness of 27.16 mag/arcsec^2) at 107 Mpc. With a stellar mass of ~4x10^8 Msun and a Re=6.9 kpc, this is the most massive and extended galaxy with such properties discovered so far. This object is ten times fainter and three times larger than known ultra-diffuse galaxies of similar stellar mass. With an estimated age of ~9+-3 Gyr, the existence of this extreme object confirms that nature can create extremely low-density extended galaxies and keep them alive for a significant period of time.