We present a new and efficient algorithm for finding point sources inthe photon event data stream from the Fermi Gamma-Ray Space Telescope,FermiFAST. The key advantage of FermiFAST is that it constructs acatalogue of potential sources very fast by arranging the photon data ina hierarchical data structure. Using this structure, FermiFAST rapidlyfinds the photons that could have originated from a potential gamma-raysource. It calculates a likelihood ratio for the contribution of thepotential source using the angular distribution of the photons withinthe region of interest. It can find within a few minutes the mostsignificant half of the Fermi Third Point Source catalogue (3FGL) withnearly 80 per cent purity from the 4 yr of data used to construct thecatalogue. If a higher purity sample is desirable, one can achieve asample that includes the most significant third of the Fermi 3FGL withonly 5 per cent of the sources unassociated with Fermi sources. Outsidethe Galactic plane, all but eight of the 580 FermiFAST detections areassociated with 3FGL sources. And of these eight, six yield significantdetections of greater than 5σ when a further binned likelihoodanalysis is performed. This software allows for rapid exploration of theFermi data, simulation of the source detection to calculate theselection function of various sources and the errors in the obtainedparameters of the sources detected.