We present a catalog of 38 young solar analogs within 25 pc, stars that are uniquely well suited for observations of their circumstellar environments to improve our understanding of conditions within the solar system during the Hadean/early Archean eons (prior to 3.8 Gyr ago). These G and early K stars were selected from the Hipparcos astrometric catalog based on lack of known stellar companions within 800 AU, bolometric luminosities close to that of the zero-age Sun and consistent with the zero-age main sequence, and ROSAT X-ray luminosities commensurate with the higher rotation rate and level of dynamo-driven activity in solar-mass stars less than 0.8 Gyr old. While many of these objects have been previously identified, this sample is novel in two respects: The selection criteria specifically consider the planetary environment, and the selection is uniform and all-sky. The X-ray emission from these young analogs is spectrally soft and consistent with a coronal origin. Calcium H and K emission, rotation periods, lithium abundances, and kinematics support an age range of 0.2-0.8 Gyr for most of these stars. Three stars have exceptionally high space motions with respect to the local standard of rest and may be old disk or halo stars that are anomalously X-ray luminous.