  The previous proposal (by two of us) of chain inflation with the QCD axion is
shown to fail. The proposal involved a series of fast tunneling events, yet
here it is shown that tunneling is too slow. We calculate the bubble nucleation
rates for phase transitions in the thick wall limit, approximating the barrier
by a triangle. A similar problem arises in realization of chain inflation in
the string landscape that uses series of minima along the monodromy staircase
around the conifold point. The basic problem is that the minima of the
potential are too far apart to allow rapid enough tunneling in these two
models. We entertain the possibility of overcoming this problem by modifying
the gravity sector to a Brans-Dicke theory. However, one would need extremely
small values for the Brans-Dicke parameter. Many successful alternatives exist,
including other "axions" (with mass scales not set by QCD) or potentials with
comparable heights and widths that do not suffer from the problem of slow
tunneling and provide successful candidates for chain inflation.
