A chapel on this site that was dedicated as the Cappella di San Lorenzo was documented in 1291, when it belonged to San Lorenzo: the canons restored it in 1321-9. 

The Confraternita dei Raccomandati di S. Maria di Prato, which used the chapel, was first documented in 1365.  This organisation was absorbed by the Confraternita del Gonfalone, Rome in the 16th century.

The interior was restored in 1770.

The inscription on the facade records its restoration in 1808: the new facade was designed by Lorenzo Cecconi.

The confraternity was suppressed in 1860, and the church now belongs to the Commune.  It was restored after the earthquake in 1997, and opened in 2009 for use as an auditorium and as the headquarters of the Centro Studi Europeo di Musica Medievale “Adolfo Broegg”.  It houses a permanent exhibition of medieval musical instruments. 

Among the frescoes revealed during the recent restoration was a fragment (17th century) of a Madonna di Costantinopoli.

This video clip gives a good idea of the interior.