We present results from a new incoherent-beam fast radio burst (FRB) search on the Canadian Hydrogen Intensity Mapping Experiment (CHIME) Pathfinder. Its large instantaneous field of view (FoV) and relative thermal insensitivity allow us to probe the ultra-bright tail of the FRB distribution, and to test a recent claim that this distribution's slope, , is quite small. A 256-input incoherent beamformer was deployed on the CHIME Pathfinder for this purpose. If the FRB distribution were described by a single power law with = 0.7, we would expect an FRB detection every few days, making this the fastest survey on the sky at present. We collected 1268 hr of data, amounting to one of the largest exposures of any FRB survey, with over 2.4 × 105 deg2 hr. Having seen no bursts, we have constrained the rate of extremely bright events to <13 sky−1 day−1 above for τ between 1.3 and 100 ms, at 400-800 MHz. The non-detection also allows us to rule out 0.9 with 95% confidence, after marginalizing over uncertainties in the GBT rate at 700-900 MHz, though we show that for a cosmological population and a large dynamic range in flux density, is brightness dependent. Since FRBs now extend to large enough distances that non-Euclidean effects are significant, there is still expected to be a dearth of faint events and relative excess of bright events. Nevertheless we have constrained the allowed number of ultra-intense FRBs. While this does not have significant implications for deeper, large-FoV surveys like full CHIME and APERTIF, it does have important consequences for other wide-field, small dish experiments.