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IC 10 X-1 belongs to the extremely rare class of Wolf-Rayet + black hole binary stellar system comma and is a valuable laboratory for understanding massive star evolution comma black hole formation comma and the effects of X-ray irradiation on stellar winds - but only if we know the mass of the black hole. Black hole masses in these systems have proven notoriously difficult to measure with ground-based optical spectroscopy only Hubble FUV spectroscopy currently capable of achieving a black hole mass measurement comma as was demonstrated for the twin system NGC 300 X-1 (HST program #15999). With a well-constrained orbital period (1.45175d) comma full X-ray coverage with Chandra comma XMM-Newton comma and NuSTAR comma and copious quantities of archival Gemini spectroscopy available comma FUV spectroscopy that samples the binary orbital period is the only missing piece of the black hole mass-puzzle for IC 10 X-1. We request 10 orbits with COS-G140L to constrain the mass of the black hole in IC 10 X-1 comma which will have far-reaching consequences for understanding black formation and for constraining future evolutionary pathways (including the possibility of compact object-merger events) of massive binary stellar systems.