There are two scenic roads in
Canyon de Chelly National Monument; Indian Reservation (IR) 7 from Chinle along the south rim of the canyon, and IR 64 along the north rim - of Canyon del Muerto, which is one of four main gorges in the canyon system. A number of rough tracks cross the reservation backcountry and lead to other canyon overlooks, but travel on these requires a Navajo permit and/or guide.
PDF format map of Canyon de Chelly National Monument, from the National Park Service (444 kb)