The Rabbit Ears are a pair of mountain peaks in northeastern New Mexico, United States, 8 kilometres north of the city of Clayton. The two peaks were a distinctive landmark along the Cimarron Cutoff of the Santa Fe Trail, a major route for westbound settlers in the 19th century. The formation was designated a National Historic Landmark in 1963. The …The Rabbit Ears are a pair of mountain peaks in northeastern New Mexico, United States, 8 kilometres north of the city of Clayton. The two peaks were a distinctive landmark along the Cimarron Cutoff of the Santa Fe Trail, a major route for westbound settlers in the 19th century. The formation was designated a National Historic Landmark in 1963. The name is that of a Native American chief who was killed here in a battle with the Spanish in 1717.