I found this:
"Following the execution of Andraste, her disciple Havard retrieved her remains and carried them back to her homeland. There, her followers interred her ashes among the mountains, building a temple which became a refuge for Andrastians in Alamarri lands.
The temple was eventually abandoned, however, and became the sanctum of the Cult of Andraste, a society composed of the violent, dragon-worshiping inhabitants of the Village of Haven. The Temple is built into the mountain itself, extending deep into its caverns, which lead to the Mountain Top."
"The Chantry is the dominant religious organization in Thedas. It is based on the Chant of Light, a series of teachings written by Andraste, the prophet of the Maker, and was founded by Kordillus Drakon, the first emperor of Orlais. Its followers are known as Andrastians. "Chantric" is also an acceptable adjective to refer to something or someone that is of the Chantry religion."
I don't think the Chantry built that Temple. Kordillus Drakon I was the founder of the Chantry and first emperor of the Orlesian Empire.