  Recent studies of accretion onto supermassive black hole binaries suggest
that much, perhaps most, of the matter eventually accretes onto one hole or the
other. If so, then for binaries whose inspiral from ~1 pc to 0.001 - 0.01 pc is
driven by interaction with external gas, both the binary orbital axis and the
individual black hole spins can be reoriented by angular momentum exchange with
this gas. Here we show that, unless the binary mass ratio is far from unity,
the spins of the individual holes align with the binary orbital axis in a time
few-100 times shorter than the binary orbital axis aligns with the angular
momentum direction of the incoming circumbinary gas; the spin of the secondary
aligns more rapidly than that of the primary by a factor ~(m_1/m_2)^{1/2}>1.
Thus the binary acts as a stabilizing agent, so that for gas-driven systems,
the black hole spins are highly likely to be aligned (or counteraligned if
retrograde accretion is common) with each other and with the binary orbital
axis. This alignment can significantly reduce the recoil speed resulting from
subsequent black hole merger.
