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The black holes (BH) in merging BH-BH binaries are likely progeny of binary O stars. Their properties, including their spins, will be strongly influenced by the evolution of their progenitor Ostars. The remarkable observation that many singleOstars spin very rapidly can be explained if they accreted angular momentum from a mass-transferring, O-type or Wolf-Rayet (WR) companion before that star blew up as a supernova. To test this prediction, we have measured the spin rates of eight O stars in WR + O binaries, increasing the total sample size of such O stars' measured spins from 2 to 10. Polarimetric and other determinations of these systems' sin i allow us to determine an average equatorial rotation velocity from He I (He II) lines of ve = 348 (173) km s-1 for these O stars, with individual star's ve from He I (He II) lines ranging from 482 (237) to 290 (91) km s-1. We argue that the ~100 per cent difference between He I and He II speeds is due to gravity darkening. Supersynchronous spins, now observed in all 10 O stars in WR + O binaries where it has been measured, are strong observational evidence that Roche lobe overflow mass transfer from a WR progenitor companion has played a critical role in the evolution of WR + OB binaries. While theory predicts that this mass transfer rapidly spins up the O-type mass gainer to a nearly breakup rotational velocity of ve ~ 530 km s-1, the observed average ve of the O-type stars in our sample is 65 per cent of that speed. This demonstrates that, even over the relatively short WR-phase time-scale, tidal and/or other effects causing rotational spin-down must be efficient. A challenge to tidal synchronization theory is that the two longest period binaries in our sample (with periods of 29.7 and 78.5 d) unexpectedly display supersynchronous rotation. [ABSTRACT FROM AUTHOR]