We present radio images within 30" of Sgr A* based on recent VLA observations at 34 GHz with 7.8 {mu}Jy sensitivity and resolution of ~88x46 mas. We report 44 partially resolved compact sources clustered in two regions in the E arm of ionized gas that orbits Sgr A*. These sources have size scales ranging between ~50 and 200 mas (400-1600 AUs), and a bow-shock appearance facing the direction of Sgr A*. Unlike the bow-shock sources previously identified in the near-IR but associated with massive stars, these 34 GHz sources do not appear to have near-IR counterparts at 3.8 {mu}m. We interpret these sources as a candidate population of photoevaporative protoplanetary disks (proplyds) that are associated with newly formed low mass stars with mass loss rates ~10^-7^-10^-6^ M_{sun}_/yr and are located at the edge of a molecular cloud outlined by ionized gas. The disks are externally illuminated by strong Lyman continuum radiation from the ~100 OB and WR massive stars distributed within 10" of Sgr A*. The presence of proplyds implies current in situ star formation activity near Sgr A* and opens a window for the first time to study low mass star, planetary, and brown dwarf formations near a supermassive black hole. The video abstract was created from a WorldWide Telescope tour file, which is available for download. Viewing the file requires a Windows PC with the WorldWide Telescope desktop client available at worldwidetelescope.org.