Massive O and early B stars are important markers of recent star formation and exert a significant influence on their environments during their short lives via photoionization and winds and when they explode as supernovae. In the Milky Way, they can be detected at great distances but often lie behind large dust columns, making detection at short wavelengths difficult. In this study, the use of the less extinguished far-red spectrum (8400-8800 {AA}) for radial velocity measurement is examined. Results are reported for a sample of 164 confirmed OB stars within a 2{deg} field positioned on the Carina Arm. Most stars are at distances between 3 and 6 kpc, and Westerlund 2 is at the field edge. The measured radial velocities have errors concentrated in the 3-10 km.s^-1^ range, with a systematic uncertainty of 2-3 km.s^-1^. These are combined with Gaia-mission astrometry to allow full space motions to be constructed. Up to 22 stars are likely to be runaways, although 8 of them are as likely to be interloping (so far undetected) binaries. The mean azimuthal motion of the sample fits in with recent measurements of Galactic disc rotation. In the Galactocentric radial direction, the mean motion indicates modest infall at a speed of ~10 km.s^-1^. This experiment shows that weak Paschen lines in the far-red can yield credible radial velocity determination, offering the prospect of exploring OB-star kinematics over much more of the Galactic disc than has hitherto been possible.