The dedication is to St Thecla.
Do not confuse the chapel with the Catacomba di Santa Tecla, which is a long way away. Also, the Tecla in the catacombs was a completely different person.
The original church was attached to one of the several monasteries clustered around the old San Pietro at the start of the Middle Ages. The first reference to this is during the reign of Pope John XIX (1024-32), and it is also mentioned in the reign of Pope Benedict IX (1032-48). It was located somewhere on the Borgo di Santo Spirito.
Armellini claims that the last reference to this institution as a working monastery is in the reign of Pope Urban VIII (1623-44), but this must be a mistake.
The present chapel is the descendent of a church built in 1592 by Pope Clement VIII for the exclusive use of the religious sisters nursing the patients in the Ospedale di Santo Spirito. It was located in a courtyard called the Cortile delle Balie, and was erected because the previous facilities for these sisters (referred to in the sources as moniale or zitelle, although they were not nuns) were inadequate. It is obvious that there was no continuity with the ancient church already mentioned.
This church was replaced in turn by the present chapel, built as part of the Conservatorio di Santa Tecla in 1675 as a dedicated house of residence for the sisters. The new chapel was not on the site of the 16th century church, described as "nearby" (prope).
The entrance to the Conservatorio is just north of the Porta Santo Spirito, on the east side. At the far end of the entrance passage is a trapezoidal courtyard. The chapel entrance is in the south-east corner.
The chapel itself does not have a separate architectural identity, but is a simple rectangular layout in a larger building.