Compact binary systems can provide us with unique information on astrophysical particle acceleration and cosmic ray production. However, only five binary systems have ever been observed in TeV $gamma$ rays. The High Altitude Water Cherenkov (HAWC) Observatory has high uptime (duty cycle $>95%$) and a wide field of view (2 sr), making it well-suited for observing transient sources such as binaries. Using two years of data from HAWC, we have searched for TeV emission from three known TeV binary systems in the field of view and twenty-eight TeV binary candidates. We have searched the HAWC data for evidence of orbital modulation or flares from these objects, and report estimates of their $gamma$-ray flux.
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