We calculate the prompt X-ray emission as a function of the viewing angle f
or beamed gamma-ray burst (GRB) sources. Prompt X-rays are inevitable owing
to the less highly blueshifted photons emitted at angles greater than or s
imilar to 1/y relative to the beam symmetry axis, where gamma is the expans
ion Lorentz factor. The observed flux depends on the combinations gamma Del
ta theta and gamma theta(v), where Delta theta is the beaming angle and the
ta(v) is the viewing angle. We use the observed source counts of gamma-ray-
selected GRBs to predict the minimum detection rate of prompt X-ray bursts
as a function of limiting sensitivity. We compare our predictions with the
results from the Ariel 5 catalog of fast X-ray transients and find that Ari
el's sensitivity is not great enough to place significant constraints on ga
mma and Delta theta. We estimate that a detector with fluence limit similar
to 10(-7) ergs cm(-2) in the 2-10 keV channel will be necessary in order t
o distinguish between geometries. Because the X-ray emission is simultaneou
s with the GRB emission, our predicted constraints do not involve any model
assumptions about the emission physics hut simply follow from special rela
tivistic considerations.