We investigate the onset of thermalization and quantum chaos in finite one-dimensional gapped systems
of hard-core bosons. Integrability in these systems is broken by next-nearest-neighbor repulsive interactions,
which also generate a superfluid to insulator transition. By employing full exact diagonalization, we study chaos
indicators and few-body observables. We show that with increasing system size, chaotic behavior is seen over
a broader range of parameters and, in particular, deeper into the insulating phase. Concomitantly, we observe
that, as the system size increases, the eigenstate thermalization hypothesis extends its range of validity inside
the insulating phase and is accompanied by the thermalization of the system.