We report on the unprecedented red supergiant (RSG) population of a massive young cluster, located at the base of the Scutum-Crux Galactic arm. We identify candidate cluster RSGs based on 2MASS photometry and medium-resolution spectroscopy. With follow-up high-resolution spectroscopy, we use CO band-head equivalent width and high-precision radial velocity measurements to identify a core grouping of 26 physically associated RSGs-the largest such cluster known to date. Using the stars' velocity dispersion and their inferred luminosities in conjunction with evolutionary models, we argue that the cluster has an initial mass of ~40,000 Msolar and is therefore among the most massive in the galaxy. Further, the cluster is only a few hundred parsecs away from the cluster of 14 RSGs recently reported by Figer at al.. These two RSG clusters represent 20% of all known RSGs in the Galaxy, and now offer the unique opportunity to study the presupernova evolution of massive stars, and the blue- to red-supergiant ratio at uniform metallicity. We use GLIMPSE, MIPSGAL, and MAGPIS survey data to identify several objects in the field of the larger cluster which seem to be indicative of recent regionwide starburst activity at the point where the Scutum-Crux arm intercepts the Galactic bulge. Future abundance studies of these clusters will therefore permit the study of the chemical evolution and metallicity gradient of the Galaxy in the region where the disk meets the bulge.