The Church can be built after researching Monotheism. It costs 66,000 Gold and 45,000 Supplies to be built. It provides 520 Happiness, which was the largest (per tile) for all the 3x3 sized buildings. This had been until Industrial Age was added to the game. The best update for the Church is Saloon which has the best Efficiency (Happiness per tile). However, the Saloon is a building of the Industrial Age.
Church is the most expensive of all buildings in High Middle Ages.