As early as 10 Gyr ago, galaxies with more than 1011 M ☉ of stars already existed. While most of these massive galaxies must have subsequently transformed through on-going star formation and mergers with other galaxies, a small fraction (lsim0.1%) may have survived untouched until today. Searches for such relic galaxies, useful windows to explore the early universe, have been inconclusive to date: galaxies with masses and sizes like those observed at high redshift (M sstarf >~ 1011 M ☉ Re <~ 1.5 kpc) have been found in the local universe, but their stars are far too young for the galaxy to be a relic galaxy. This paper explores the first case of a nearby galaxy, NGC 1277 (at a distance of 73 Mpc in the Perseus galaxy cluster), which fulfills many criteria to be considered a relic galaxy. Using deep optical spectroscopy, we derive the star formation history along the structure of the galaxy: the stellar populations are uniformly old (>10 Gyr) with no evidence for more recent star formation episodes. The metallicity of their stars is super-solar ([Fe/H] = 0.20 ± 0.04 with a smooth decline toward the outer regions) and α-enriched ([α/Fe] = 0.4 ± 0.1). This suggests a very short formation time scale for the bulk of the stars in this galaxy. This object also rotates very fast (V rot ~ 300 km s–1) and has a large central velocity dispersion (σ > 300 km s–1). NGC 1277 allows the exploration in full detail of properties such as the structure, internal dynamics, metallicity, and initial mass function as they were at ~10-12 Gyr ago when the first massive galaxies were built.