Evolution of inhomogeneities in the axion field around the QCD epoch i
s studied numerically, including for the first time important nonlinea
r effects. It is found that perturbations on scales corresponding to c
ausally disconnected regions at T approximately 1 GeV can lead to very
dense axion clumps, with present density rho(a) greater than or simil
ar to 10(-8) g cm-3. This is high enough for the collisional 2a --> 2a
process to lead to Bose-Einstein relaxation in the gravitationally bo
und clumps of axions, forming Bose stars.