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 the recent result that the Bardeen–Petterson effect causes counteralignment 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 Jd are no larger than the angular momentum of the hole, Jh. 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, ≲0.1 pc.