We argue that primordial black holes in the early universe can provide an efficient resolution of the Brustein-Steinhardt moduli overshoot problem in string cosmology. When the universe is created near the Planck scale, all the available states in the theory are excited by strong interactions and cosmological particle production. The heavy states are described in the low energy theory as a gas of electrically and magnetically charged black holes. This gas of black holes quickly captures the moduli which appear in the relation between black hole masses and charges, and slows them down with their vevs typically close to the Planck scale. From there, the modulus may slowly roll into a valley with a positive vacuum energy, where inflation may begin. The black hole gas will redshift away in the course of cosmic expansion, as inflation evicts black holes out of the horizon.

14 pages latex, 7 .eps figures; v2: added references and a few comments