Background: The discrepancy between proton electromagnetic form factors extracted using unpolarized and polarized scattering data is believed to be a consequence of two-photon exchange (TPE) effects. However, the calculations of TPE corrections have significant model dependence, and there is limited direct experimental evidence for such corrections. Purpose: The TPE contributions depend on the sign of the lepton charge in e±p scattering, but the luminosities of secondary positron beams limited past measurement at large scattering angles, where the TPE effects are believe to be most significant. We present the results of a new experimental technique for making direct e ±p comparisons, which has the potential to make precise measurements over a broad range in Q2 and scattering angles. Methods: We use the Jefferson Laboratory electron beam and the Hall B photon tagger to generate a clean but untagged photon beam. The photon beam impinges on a converter foil to generate a mixed beam of electrons, positrons, and photons. A chicane is used to separate and recombine the electron and positron beams while the photon beam is stopped by a photon blocker. This provides a combined electron and positron beam, with energies from 0.5 to 3.2 GeV, which impinges on a liquid hydrogen target. The large acceptance CLAS detector is used to identify and reconstruct elastic scattering events, determining both the initial lepton energy and the sign of the scattered lepton. Results: The data were collected in two days with a primary electron beam energy of only 3.3 GeV, limiting the data from this run to smaller values of Q2 and scattering angle. Nonetheless, this measurement yields a data sample for e±p with statistics comparable to those of the best previous measurements. We have shown that we can cleanly identify elastic scattering events and correct for the difference in acceptance for electron and positron scattering. Because we ran with only one polarity for the chicane, we are unable to study the difference between the incoming electron and positron beams. This systematic effect leads to the largest uncertainty in the final ratio of positron to electron scattering: R=1.027±0. 005±0.05 for=0.206 GeV2 and 0.830≤≤0.943. Conclusions: We have demonstrated that the tertiary e± beam generated using this technique provides the opportunity for dramatically improved comparisons of e±p scattering, covering a significant range in both Q2 and scattering angle. Combining data with different chicane polarities will allow for detailed studies of the difference between the incoming e+ and e- beams. © 2013 American Physical Society.