Independent Traditionalist Chapels

Independent Traditionalist Chapels
Question from on 07-31-2007:
Dario Cardinal Castrillon Hoyos has said the SSPX is not in schism several times in the past two years, but I'd like to know about the Independent Traditionalist Chapels that operate separate from the local diocese.

The traditionalists are telling people they are "private oratories," but would they be considered schismatic for illicitly holding Tridentine Masses without the bishop's authority? or for refusing to submit to the local bishop?

I have an independent chapel outside of Washington, D.C., in mind, because the priest there supposedly is a runaway priest of the Archdiocese of Baltimore who has setup shop in the Diocese of Arlington.
Answer by Rev. Mark J. Gantley, JCL on 07-31-2007:
No priest is permitted to set up his own little church and do whatever he wants. He must be under the authority of the local diocesan bishop as well as the pope or else it is not truly a Catholic celebration.

Hopefully, with the new norms promulgated by the pope with regard to celebrating the 1962 Roman Missal, the need for such illicit celebrations will diminish greatly.