  Cosmological $\alpha$-attractors are observationally favored due to the
asymptotic flatness of the potential. Since its flatness induces the negative
pressure even after inflation, the coherent oscillation of the inflaton field
could fragment into quasi-stable localized objects called I-balls (or
"oscillons"). We investigated the possibility of I-ball formation in E-models
of $\alpha$-attractors. Using linear analysis and the lattice simulations, we
find that for $\alpha\lesssim10^{-3}$, the inflaton feels the negative pressure
long enough and actually fragments into I-balls.
