We present new Chandra and Hubble/COS observations to the Wolf-Rayet + black hole binary NGC 300 X-1. We combined our new X-ray observation with twenty years worth of archival data from Chandra and XMM-Newton data to determine the most precise orbital period known for the system: 32.7921 ± 0.0003 hr. This highly precise orbital period has allowed us to calculate the orbital phase at which our new Hubble/COS G140L observations were obtained, and to update the orbital phase at which previously published optical spectroscopy were performed. We investigate the properties of the He II emission lines at 1640 and 4686 Angstroms, and find the radial velocity variations of both He II lines lag the expected motion of the black hole by ~0.3 in phase (equivalent to ~10 hours). This result is similar to observations of another Wolf-Rayet + black hole binary, IC 10 X-1, and definitively shows that He II is not a reliable indicator of black hole mass in the system.