Iglesia La Compañía de Jesus literally means church of the Society of Jesus. Locally, most refer to it simply as La Compañía.
As with many ornate houses of worship, this one took generations to complete -- 160 years to be exact. The baroque style of art inside is well worth seeing, but no photography is permitted.
In recent years, fire destroyed part of the interior, but restoration projects have been diligent. Admission is $2 and includes a guided tour in English or Spanish.