Over 50 years ago, Anderson and Blount discussed symmetry-allowed polar distortions in metals, spawning the idea that a material might be simultaneously metallic and ferroelectric. While many studies have ever since considered such or similar situations, actual ferroelectricity--that is, the existence of a switchable intrinsic electric polarization--has not yet been attained in a metal, and is in fact generally deemed incompatible with the screening by mobile conduction charges. Here we refute this common wisdom and show, by means of first-principles simulations, that native metallicity and ferroelectricity coexist in the layered perovskite Bi5Ti5O17. We show that, despite being a metal, Bi5Ti5O17 can sustain a sizable potential drop along the polar direction, as needed to reverse its polarization by an external bias. We also reveal striking behaviours, as the self-screening mechanism at work in thin Bi5Ti5O17 layers, emerging from the interplay between polar distortions and carriers in this compound.