LTT 1445 is a hierarchical triple M-dwarf star system located at a distance of 6.86 pc. The primary star LTT 1445A (0.257 M-circle dot) is known to host the transiting planet LTT 1445Ab with an orbital period of 5.36 days, making it the second-closest known transiting exoplanet system, and the closest one for which the host is an M dwarf. Using Transiting Exoplanet Survey Satellite data, we present the discovery of a second planet in the LTT 1445 system, with an orbital period of 3.12 days. We combine radial-velocity measurements obtained from the five spectrographs, Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations, High Accuracy Radial Velocity Planet Searcher, High-Resolution Echelle Spectrometer, MAROON-X, and Planet Finder Spectrograph to establish that the new world also orbits LTT 1445A. We determine the mass and radius of LTT 1445Ab to be 2.87 +/- 0.25 M-circle plus and 1.304(-0.060)(+0.067) R-circle plus, consistent with an Earth-like composition. For the newly discovered LTT 1445Ac, we measure a mass of 1.54(-0.19)(+0.20) M-circle plus and a minimum radius of 1.15 R-circle plus, but we cannot determine the radius directly as the signal-to-noise ratio of our light curve permits both grazing and nongrazing configurations. Using MEarth photometry and ground-based spectroscopy, we establish that star C (0.161 M-circle dot) is likely the source of the 1.4 day rotation period, and star B (0.215 MY circle dot) has a likely rotation period of 6.7 days. We estimate a probable rotation period of 85 days for LTT 1445A. Thus, this triple M-dwarf system appears to be in a special evolutionary stage where the most massive M dwarf has spun down, the intermediate mass M dwarf is in the process of spinning down, while the least massive stellar component has not yet begun to spin down.