We report the first measurement of the vector analyzing power in inclusive transversely polarized elastic electron- proton scattering at Q(2) = 0.1 (GeV/c)(2) and large scattering angles. This quantity must vanish in the single virtual photon exchange, plane-wave impulse approximation for this reaction, and can therefore provide information on two photon exchange amplitudes for electromagnetic interactions with hadronic systems. The observable we have measured is driven by the imaginary part of the two photon exchange amplitude, the hadronic side of which is simply the Compton amplitude for the proton with two virtual photons. We find a small but nonzero value of A = -15.4 +/- 5.4 ppm.