  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, $\alpha\equiv-\frac{\partial \log
N}{\partial \log S}$, 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 $\alpha=0.7$, we would expect an FRB
detection every few days, making this the fastest survey on sky at present. We
collected 1268 hours of data, amounting to one of the largest exposures of any
FRB survey, with over 2.4\,$\times$\,10$^5$\,deg$^2$\,hrs. Having seen no
bursts, we have constrained the rate of extremely bright events to
$<\!13$\,sky$^{-1}$\,day$^{-1}$ above $\sim$\,220$\sqrt{(\tau/\rm ms)}$ Jy\,ms
for $\tau$ between 1.3 and 100\,ms, at 400--800\,MHz. The non-detection also
allows us to rule out $\alpha\lesssim0.9$ 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, $\alpha$ 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.
