The High-Altitude Water Cherenkov (HAWC) Observatory records the air showers produced by cosmic rays and gamma rays at a rate of about 20 kHz. While the events observed by HAWC are 99.9% hadronic cosmic rays, this background can be strongly suppressed using topological cuts that preferentially select electromagnetic air showers. Using this capability of HAWC, we can create a sample of air showers dominated by gamma rays and cosmic electrons and positrons. HAWC is one of the few operating observatories capable of measuring showers produced by electron and positron primaries above 1 TeV, and can record these showers from two-thirds of the sky each day. We describe the sensitivity of HAWC to leptonic cosmic rays, and discuss prospects for the measurement of the combined $e^+e^-$ flux and possible approaches for positron and electron charge separation with the HAWC detector.
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