We have measured the beam-normal single-spin asymmetry in elastic scattering of transversely polarized 3 GeV electrons from unpolarized protons at Q2=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. An provides a direct probe of the imaginary component of the 2γ exchange amplitude, the complete description of which is important in the interpretation of data from precision electron-scattering experiments.