This is the church of Santa María Tonantzintla, Puebla, a supreme example of barroco novohispano, or what they also call indigenous baroque. The style is basically a fusion of colonial architecture with pre-Hispanic design principles, and the site most often associated with indigenous baroque is Santo Domingo, in Oaxaca.
I'd argue Santa María Tonantzintla is on another level.
Friends had described it beforehand as the "Indian church" or the "church built by Indians," and indeed, on first sight, it feels indigenous, uniquely not a totem to Catholic power. The facade of the Tonantzintla church -- Nahautl for "the place of our little mother" or "lugar de nuestra madrecita" -- looks like how we imagine the exteriors of pyramids looked, not just ruins of stone but brightly colored and textured with dense ornamentation.
The saints and angels that adorn the exterior and interior niches are formed, vaguely, in the manner of the old Aztec sculptures.
Here's a closer view of the facade, and here's about as close a shot I was able to get inside the nave, as the church was packed with parishioners for a special Mass of some sort on the Sunday we visited. Photos are not allowed inside Santa María Tonantzintla, a rule I suppose is meant to preserve the maximal barroco novohispano decorative work that covers just about every inch of wall-space in the interior. But here's the Google Images scan, and here's an amateur video. Don't the walls look alive, unreal?
The Puebla state government says construction began on Santa María Tonantzintla in the 16th Century, by indigenous artisans. I was able to find very little information on the church's history otherwise. Apparently the local community is fiercely protective of the site, declaring that it is autonomous from the diocese of Puebla.
We happened to visit during the festival de queso in the pueblo. Mmmmm. Every outdoor space, packed with food and smells and vendors. We picked up some nopal and cheese ice cream, and then headed over to Chipilo.