The massive black hole + Wolf-Rayet binary IC10 X-1 was observed in a series of 10 Chandra and 2 XMM-Newton observations spanning 2003-2012, showing consistent variability around 7×10 37 erg s −1 , with a spectral hardening event in 2009. We phase-connected the entire light-curve by folding the photon arrival times on a series of trial periods spanning the known orbital period and its uncertainty, refining the X-ray period to P = 1.45175(1)d. The duration of minimum-flux in the X-ray eclipse is ∼5 hr which together with the optical radial velocity curve for the companion yields a radius for the eclipsing body of 8-10R for the allowed range of masses. The orbital separation (a 1 + a 2 ) = 18.5-22R then provides a limiting inclination i > 63 • for total eclipses to occur. The eclipses are asymmetric (egress duration ∼ 0.9hr) and show energy dependence, suggestive of an accretiondisk hotspot and corona. The eclipse is much (∼5X) wider than the 1.5-2R WR star, pointing to absorption/scattering in the dense wind of the WR star. The same is true of the close analog NGC 300 X-1. RV measurements of the He II [λλ4686] line from the literature show a phase-shift with respect to the X-ray ephemeris such that the velocity does not pass through zero at mid-eclipse. The X-ray eclipse leads inferior conjunction of the RV curve by ∼90 • , so either the BH is being eclipsed by a trailing shock/plume, or the He II line does not directly trace the motion of the WR star and instead originates in a shadowed partially-ionized region of the stellar wind.