LTT1445 is a hierarchical triple M-dwarf star system located at a distance of 6.86pc. The primary star LTT1445A (0.257M{sun}) is known to host the transiting planet LTT1445Ab with an orbital period of 5.36days, 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 LTT1445 system, with an orbital period of 3.12days. 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 LTT1445A. We determine the mass and radius of LTT1445Ab to be 2.87{+/-}0.25M{Earth} and 1.304_-0.060_^+0.067^R{Earth}, consistent with an Earth-like composition. For the newly discovered LTT 1445Ac, we measure a mass of 1.54_-0.19_^+0.20^M{Earth} and a minimum radius of 1.15R{Earth}, 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 (0.161M{sun}) is likely the source of the 1.4day rotation period, and star B (0.215M{sun}) has a likely rotation period of 6.7days. We estimate a probable rotation period of 85days for LTT1445A. 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.