We present the discovery from Transiting Exoplanet Survey Satellite (TESS) data of LTT 1445Ab. At a distance of 6.9 pc, it is the second nearest transiting exoplanet system found to date, and the closest one known for which the primary is an M dwarf. The host stellar system consists of three mid-to-late M dwarfs in a hierarchical configuration, which are blended in one TESS pixel. We use MEarth data and results from the Science Processing Operations Center data validation report to determine that the planet transits the primary star in the system. The planet has a radius of 1.38(-0.12)(+0.13) R-circle plus, an orbital period of 5.35882(-0.00031)(+0.00030) days, and an equilibrium temperature of 433(-27)(+28) K. With radial velocities from the High Accuracy Radial Velocity Planet Searcher, we place a 3 sigma upper mass limit of 8.4 M-circle plus on the planet. LTT 1445Ab provides one of the best opportunities to date for the spectroscopic study of the atmosphere of a terrestrial world. We also present a detailed characterization of the host stellar system. We use high-resolution spectroscopy and imaging to rule out the presence of any other close stellar or brown dwarf companions. Nineteen years of photometric monitoring of A and BC indicate a moderate amount of variability, in agreement with that observed in the TESS light-curve data. We derive a preliminary astrometric orbit for the BC pair that reveals an edge-on and eccentric configuration. The presence of a transiting planet in this system hints that the entire system may be co-planar, implying that the system may have formed from the early fragmentation of an individual protostellar core.