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. We present the results of a new experimental
technique for making direct $e^\pm p$ comparisons, which has the potential to
make precise measurements over a broad range in $Q^2$ and scattering angles. We
use the Jefferson Lab 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. 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 $Q^2$ and scattering angle. Nonetheless, this measurement
yields a data sample for $e^\pm p$ 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. The final ratio of positron to electron scattering:
$R=1.027\pm0.005\pm0.05$ for $=0.206$ GeV$^2$ and $0.830\leq \epsilon\leq
0.943$.