Canyon de Chelly National Monument is located on Navaho reservation land. People have lived in this canyon for nearly 5000 years and are still living there. There is only one hiking trail, White House Trail, which ends at the White House Ruins and is not dog friendly. One way is 1.25 miles and descends 600 feet with lots of switchbacks. However, dogs are allowed at all ten of the overlooks which can be found on the two scenic drives. There are seven overlooks on the South Rim Drive and three on the North Rim Drive.
The canyons which make up the park, Canyon de Chelly and Canyon del Muerto, are both full of human history. Canyon tours are available but like White House Trail, they are not dog friendly. Overall the park gets a one paw rating for pet friendliness.
Their current pet regulations are found on the FAQ page at park’s website. The park map can be downloaded as well.