  We develop a model of eternal topological inflation using a racetrack
potential within the context of type IIB string theory with KKLT volume
stabilization. The inflaton field is the imaginary part of the K\"ahler
structure modulus, which is an axion-like field in the 4D effective field
theory. This model does not require moving branes, and in this sense it is
simpler than other models of string theory inflation. Contrary to
single-exponential models, the structure of the potential in this example
allows for the existence of saddle points between two degenerate local minima
for which the slow-roll conditions can be satisfied in a particular range of
parameter space. We conjecture that this type of inflation should be present in
more general realizations of the modular landscape. We also consider
`irrational' models having a dense set of minima, and discuss their possible
relevance for the cosmological constant problem.
