In 1476 on the site of the wooden Trinity Church (1412) by St. Nikon, master builders from Pskov invited for the construction work in the Moscow Kremlin erected a new 1-domed church, dedicated to the Descent of the Holy Spirit upon the Apostles. Under the dome the builders placed an open belfry. In 1608–10 during the Polish siege this church was used as a watchtower.
The Holy Spirit Church and the Trinity Cathedral form an ensemble. The frescoes in the Holy Spirit Church were executed in 1655, but in the middle of the 19th century they were replaced by oil paintings. The iconostasis was carved of rosewood by Lavra woodcarvers in 1866. In the church there are 2 temples with the holy relics of St. Maximus the Greek († 1556) and St. Anthony of Radonezh († 1877). St. Maximus the Greek was one of the most erudite men of his period who wrote many theological and polemic works. He died in the monastery and was buried here. In 1988 he was canonised. Since 1770 Moscow metropolitans were abbots of the monastery. St. Anthony was the monastery vicar in 1831–77 and canonised in 1996.