  We consider chimera states of coupled identical phase oscillators where some
oscillators are phase synchronized while others are desynchronized. It is known
that chimera states of non-locally coupled Kuramoto--Sakaguchi oscillators in
arrays of finite size are chaotic transients when the phase lag parameter
$\alpha \in (0, \pi/2)$; after a transient time, all the oscillators are phase
synchronized, with the transient time increasing exponentially with the number
of oscillators. In this work, we consider a small array of six non-locally
coupled oscillators with the phase lag parameter $\alpha \in (\pi/2, \pi)$ in
which the complete phase synchronization of the oscillators is unstable. Under
these circumstances, we observe a chimera state spontaneously formed by the
partition of oscillators into two independently synchronizable clusters of both
stable and unstable synchronous states. We provide numerical evidence
supporting that the instantaneous frequencies of the oscillators of the chimera
state are periodic functions of time with a common period, and as a result, the
chimera state is stable but not long-lived transient. We also measure the basin
stability of the chimera state and show that it can be observed for random
initial conditions when $\alpha$ is slightly larger than $\pi/2$.
