In the days before Summorum Pontificum, attending a Traditional Mass (Mass in the "Extraordinary Form" of the Roman Rite) in the Papal Basilica of Saint Peter in the Vatican could be quite a challenge, almost like playing hide-and-seek...
Since Pope Benedict XVI's measure of justice, Traditional Masses have become quite frequent early in the morning at the side altars throughout the building. Naturally, the vast majority of masses are in the Rite of Paul VI (the "Ordinary Form"), and one of the great problems found by pilgrims attached to the Traditional Roman Rite is that they often can't find the right time and place for a TLM.
We are informed of the following regular hours for Traditional Low Masses in the Vatican Basilica ("private" masses, as almost all those at side altars) for pilgrims visiting Rome. They are not necessarily the only ones at any given day, but they are available with a greater degree of certainty:
Basilica di San Pietro in Vaticano
each morning, at 7 a.m, local time
at the Altar of Pope Blessed Innocent XI [76 in the floor plan below]
and at the Altar of Saint Michael the Archangel [33 in the floor plan below]
The Basilica is closed to the general public on most Wednesday mornings due to the General Audiences of the Holy Father, and on days of special events in the building.
(click for larger view)
[Tip: Chiesa e post concilio]