  We consider the problem of growing the largest supermassive black holes from
stellar--mass seeds at high redshift. Rapid growth without violating the
Eddington limit requires that most mass is gained while the hole has a low spin
and thus a low radiative accretion efficiency. If, as was formerly thought, the
black--hole spin aligns very rapidly with the accretion flow, even a
randomly--oriented sequence of accretion events would all spin up the hole and
prevent rapid mass growth. However, using a recent result that the
Bardeen--Petterson effect causes {\it counter}alignment of hole and disc spins
under certain conditions, we show that holes can grow rapidly in mass if they
acquire most of it in a sequence of randomly oriented accretion episodes whose
angular momenta $J_d$ are no larger than the hole's angular momentum $J_h$.
Ultimately the hole has total angular momentum comparable with the last
accretion episode. This points to a picture in which the accretion is chaotic
on a lengthscale of order the disc size, that is $\la 0.1$ pc.
