We observed five clusters of upper‐level compact intracloud discharges (CIDs) moving positive charge up over land and over water in Florida. The clusters each contained 3 to 6 CIDs, and the overall cluster duration ranged from 27 to 58 s. On average, the CIDs in a given cluster occurred 11 s apart and were separated by a 3D distance of about 1.5 km. All the clustered CIDs were located above the tropopause and were likely associated with convective surges that penetrated the stratosphere. The average periodicity of CID occurrence within a cluster (every 11 s) was comparable to the periodicity at which the average cluster area is expected to be bombarded by ≥1016 eV cosmic‐ray particles (every 5 s). Each of such energetic particles gives rise to a cosmic ray shower (CRS) and, in the presence of sufficiently strong electric field over a sufficiently large distance, to a relativistic runaway electron avalanche (RREA). We infer that each of our upper‐level CIDs is likely to be caused by a CRS‐RREA traversing, at nearly the speed of light, the electrified overshooting convective surge and triggering, within a few microseconds, a multitude of streamer flashes along its path, over a distance of the order of hundreds of meters (as per the mechanism recently proposed for lightning initiation by Kostinskiy et al., 2020, https://doi.org/10.1029/2020JD033191). The upper‐level CID clustering was likely made possible by the recurring action of energetic cosmic rays and the rapid recovery of the negative screening charge layer at stratospheric altitudes.