  We have measured the beam-normal single-spin asymmetry in elastic scattering
of transversely-polarized 3 GeV electrons from unpolarized protons at Q^2 =
0.15, 0.25 (GeV/c)^2. The results are inconsistent with calculations solely
using the elastic nucleon intermediate state, and generally agree with
calculations with significant inelastic hadronic intermediate state
contributions. A_n provides a direct probe of the imaginary component of the
2-gamma exchange amplitude, the complete description of which is important in
the interpretation of data from precision electron-scattering experiments.
