Butterfly is a highly-rated canyon on the Navajo Nation. It's also been closed since the early 2000's.
First descended and explored around 2000, the canyon is long, with several enormous keeper potholes in the very beginning, and a dark section with several more moderate potholes in the end. The route can, depending on lake levels, be descended all the way to Kaibeto Creek. From there, it's a long, sandy slog back to the trailhead.
Rope grooves and fresh bolts indicate this canyon is occasionally poached. I can't recommend it. The owners frequently patrol their land looking for livestock, and there's a house on a hill overlooking the canyon. Furthermore, this canyon is explicitly stated on the Navajo Nation website to be closed. Don't poach it. Please.
If you do get permission, as we did (which was only possible because I've lived and worked on the Navajo Reservation for several years and have built relationships with locals), Butterfly is a great canyon with much to offer.