The dedication was to St Celsus and its proper name is Oratorio di San Celso, but it is universally known as San Celsino (or "little St Celsus") to distinguish it from the church of Santi Celso e Giuliano nearby.
The oratory was built in 1571 as the headquarters of the Confraternita del Santissimo Sacramento or "Confraternity of the Blessed Sacrament", instituted in the parish of Santi Celso e Giuliano. This it remained until 1984. It was then used as a charity centre by the Rome diocese, but was abandoned in 1993 and has now been deconsecrated.
The facade was restored in the 1990's to ensure its civic presence, but the future of the rest of the building is uncertain. It remains listed on the website of the Diocese, however (June 2019), which is odd.
Despite having been only an oratory, this amounts to a small free-standing church. The plan is a short rectangle, with a tiny semi-circular apse.
Because of its cramped site, the church's façade cannot be viewed properly. After restoration, it is now rendered in dull orange with white stone architectural details. The doorcase is crowned by a frieze and a triangular pediment with recessed central section, and above this is a rectangular dedicatory plaque flanked by small double volutes. The two storeys of the façade are separated by an entablature, which is supported by four rectangular pilasters with swagged Ionic capitals and high plinths. In between each pair is an arched blank niche (meant to be empty, as the bottom slopes) with scallop decoration in the conch. Above this is a blank framed rectangular tablet.The second storey has a pair of Doric pilasters above the central pair of pilasters of the first storey, and these support a segmental pediment. Very dumpy pilasters occupy the outer corners, and double volutes from the tops of these connect to the pediment and have a small window under each. A recessed blank tablet in a Baroque frame occupies the centre of this storey.
There was an 18th century fresco of the Assumption on the ceiling vault, which was peeling off and may now be lost. The artist is unknown.
The oratory had only one altar, the altarpiece of which was Christ with his Disciples at the Last Supper. This was another anonymous work, of the 17th century.