Yes! That would be the Eparchy of St. Peter in San Diego. Bishop Sarhad Yawsip was a guest last year on EWTN, where he gave a very interesting presentation on the history of the Chaldean Church. Have you attended any of their liturgies?
Southern CA is also home to a large contingent of Lebanese catholics who attend the Maronite Catholic Church. If you have the opportunity, I would recommend attending their Divine Liturgy at St. Ephrem's.
Have not attended their liturgies.
Have heard from a few how they escaped from Iraq
some years back.