We have obtained multi-epoch observations of 31 O-type stars in the Carina Nebula using the CHIRON spectrograph on the CTIO/SMARTS 1.5-m telescope . We measure their radial velocities to 1–2 km s ^ { -1 } precision and present new or updated orbital solutions for the binary systems HD 92607 , HD 93576 , HDE 303312 , and HDE 305536 . We also compile radial velocities from the literature for 32 additional O-type and evolved massive stars in the region . The combined data set shows a mean heliocentric radial velocity of 0.6 km s ^ { -1 } . We calculate a velocity dispersion of \leq 9.1 km s ^ { -1 } , consistent with an unbound , substructured OB association . The Tr 14 cluster shows a marginally significant 5 km s ^ { -1 } radial velocity offset from its neighbor Tr 16 , but there are otherwise no correlations between stellar position and velocity . The O-type stars in Cr 228 and the South Pillars region have a lower velocity dispersion than the region as a whole , supporting a model of distributed massive-star formation rather than migration from the central clusters . We compare our stellar velocities to the Carina Nebula ’ s molecular gas and find that Tr 14 shows a close kinematic association with the Northern Cloud . In contrast , Tr 16 has accelerated the Southern Cloud by 10–15 km s ^ { -1 } , possibly triggering further massive-star formation . The expansion of the surrounding \ion Hii region is not symmetric about the O-type stars in radial velocity space , indicating that the ionized gas is constrained by denser material on the far side .