The initial Galactic velocity vector for the recently discovered hyperbolic asteroid 1I/Oumuamua (A/2017 U1) is calculated for before its encounter with our solar system. The latest orbit (JPL-13) shows that Oumuamua has eccentricity > 1 at 944sigma, significance (1.19936 +- 0.00021), i.e. clearly unbound. Assuming no non-gravitational forces, the objects inbound Galactic velocity was U, V, W = -11.457, -22.395, -7.746 (+-0.009, +-0.009, +-0.011) km/s (U towards Galactic center), with total heliocentric speed 26.32 +- 0.01 km/s. When the velocity is compared to the local stars, Oumuamua can be ruled out as co-moving with any of the dozen nearest systems, i.e. it does not appear to be associated with any local exo-Oort clouds (most notably that of the Alpha Centauri triple system). Oumuamuas velocity is within 5 km/s of the median Galactic velocity of the stars in the solar neighborhood (<25 pc), and within 2 km/s of the mean velocity of the local M dwarfs. Its velocity appears to be statistically too typical for a body whose velocity was drawn from the Galactic velocity distribution of the local stars (i.e. less than 1 in 500 field stars in the solar neighborhood would have a velocity so close to the median UVW velocity). In the Local Standard of Rest frame (circular Galactic motion), Oumuamua is remarkable for showing both negligible radial (U) and vertical (W) motion, while having a slightly sub-Keplerian circular velocity (V; by ~11 km/s). These calculations strengthen the interpretation that A/2017 U1 has a distant extrasolar origin, but not among the very nearest stars. Any formation mechanism for this interstellar asteroid should account for the coincidence of Oumuamuas velocity being so close to the LSR.