In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional
α
\alpha
-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a Lévy-driven Rosenblatt random variable when the Hurst parameter satisfies
H
∈
(
1
/
2
,
1
)
H\in (1/2,1)
and
α
(
1
−
H
)
>
1
/
2
\alpha (1-H)>1/2
. This result complements the asymptotic theory for fractional stable processes.