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The Very Energetic Radiation Imaging Telescope Array System (VERITAS) Collaboration joined this program in 2018 and provides the capability to search for one particular technosignature: optical pulses of a few nanoseconds in duration detectable over interstellar distances. We report here on the analysis and results of dedicated VERITAS observations of Breakthrough Listen targets conducted in 2019 and 2020 and of archival VERITAS data collected since 2012. Thirty hours of dedicated observations of 136 targets and 249 archival observations of 140 targets were analyzed and did not reveal any signals consistent with a technosignature. The results are used to place limits on the fraction of stars hosting transmitting civilizations. We also discuss the minimum pulse sensitivity of our observations and present VERITAS observations of CALIOP: a space-based pulsed laser on board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations. 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