  We study the domain wall problem of an axion in chaotic inflation models. We
show that the production of domain walls does not occurs if the Peccei-Quinn
scalar has a flat potential and its breaking $F_{a}$ is larger than $\sim
10^{15}$GeV. We find that too large isocurvature fluctuations are produced for
such high $F_{a}$. In order for those isocurvature fluctuations to be
consistent with observations of the large scale structure of the universe, the
self-coupling constant $g$ and the breaking scale of the Peccei-Quinn scalar
should be $g \simeq (1-2.8)\times 10^{-13}$ and $F_{a} \simeq (0.6-1.5)\times
10^{15}$GeV, respectively. In particular the value of self-coupling constant is
almost the same as that required for a chaotic inflation, which strongly
suggests that the Peccei-Quinn scalar itself is an inflaton.
