Preheat the oven to 350 degrees F (175 degrees C). Prepare four 12-inch square pieces of parchment paper.

Mix together chili powder, paprika, oregano, cayenne pepper, and black pepper in a large bowl. Add chicken and toss until evenly and generously coated with spice mixture. Transfer each chicken breast to the center of a parchment square.

Wrap each chicken breast in the parchment paper like a burrito; transfer to a baking pan.

Bake in the preheated oven until chicken is no longer pink in the center and the juices run clear, about 25 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Remove from oven and let cool for 5 minutes. Unwrap chicken carefully, as the juices inside the pouch are very hot and can burn.