Begay was born in Tuba City, Arizona, on January 11, 1954. He grew up on the Navajo reservation, where he learned about traditional Navajo culture from his parents and grandparents. Begay began drawing and painting at a young age, and he soon realized that he had a talent for art.
After graduating from high school, Begay studied art at the Institute of American Indian Arts in Santa Fe, New Mexico. He then attended the University of Arizona, where he earned a Bachelor of Fine Arts degree.
Begay's paintings depict a variety of subjects, including Navajo ceremonies, rituals, and everyday life. His work is characterized by its vibrant colors, intricate patterns, and strong sense of spirituality. Begay's paintings have been praised for their beauty, their cultural significance, and their ability to capture the essence of Navajo life.
Begay's work has been exhibited in museums and galleries around the world, including the Smithsonian Institution, the Heard Museum, and the Museum of Modern Art. He has also received numerous awards, including the National Endowment for the Arts Fellowship, the Arizona Governor's Arts Award, and the Native American Art Awards.
Begay's work continues to inspire and educate viewers about Navajo culture. He is considered one of the most important Native American artists of his generation.
Begay died of cancer on August 17, 2012, in Tuba City, Arizona. He was 58 years old.