Primordial Black Holes (PBHs) are black holes that may have been created by density fluctuations in the early Universe and could be as massive as supermassive black holes or as small as the Planck scale. It is believed that a black hole has a temperature inversely proportional to its mass and will thermally emit all species of fundamental particles via Hawking Radiation. PBHs with initial masses of ~5e14 g (approximately one gigaton) should be expiring today with bursts of high-energy gamma radiation in the GeV – TeV energy range. The High Altitude Water Cherenkov (HAWC) Observatory is sensitive to particles with energies of 300 GeV – 100 TeV, which corresponds to the high end of the PBH burst spectrum. With its large instantaneous field of view of ~2 sr and a duty cycle above 95%, the HAWC Observatory is well suited to perform an all-sky search for PBH bursts. We conducted a search on 959 days of gamma-ray data from HAWC by optimizing a previous gamma-ray burst transient search to the PBH burst energy spectrum, and placed the strongest upper limits on the local PBH burst rate density at the 99% confidence level.