We report the first measurement of the vector analyzing power in inclusive transversely polarized elastic electron-proton scattering at Q2 = 0.1 (GeV/c)2 and large scattering angles. This quantity should vanish in the single virtual photon exchange, plane wave impulse approximation for this reaction, and can therefore provide information on double photon exchange amplitudes for electro- magnetic interactions with hadronic systems. We find a non-zero value of A=-15.4±5.4 ppm. No calculations of this observable for nuclei other than spin 0 have been carried out in these kinematics, and the calculation using the spin orbit interaction from a charged point nucleus of spin 0 cannot describe these data.