We calculate the prompt X-ray emission as a function of the viewing angle for beamed gamma-ray burst (GRB) sources. Prompt X-rays are inevitable owing to the less highly blueshifted photons emitted at angles 1/γ relative to the beam symmetry axis, where γ is the expansion Lorentz factor. The observed flux depends on the combinations γΔθ and γθ_v, where Δθ is the beaming angle and θ_v is the viewing angle. We use the observed source counts of γ-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 Ariel's sensitivity is not great enough to place significant constraints on γ and Δθ. We estimate that a detector with fluence limit ~10^-7 ergs cm^-2 in the 2-10 keV channel will be necessary in order to distinguish between geometries. Because the X-ray emission is simultaneous with the GRB emission, our predicted constraints do not involve any model assumptions about the emission physics but simply follow from special relativistic considerations.