The movie was based on actual events, so it is true. The movie itself, is not real, but the events are. Everyone in Texas knows about it. The real killer was Ed Gien. He was a mentally-challenged individual who robbed graves and made clothes and other items out of the skin and bones he collected. He killed two women, but he didn't cover his tracks well, and the police found one of the bodies hanging up like a carcass being butchered with some other bits apparently ready for cooking. Ed Gein never actually used a chainsaw though. He was also a cannibal (someone who eats or hunts other humans for food).
Yes, I used to have nightmares that I was a victim running from him. I'm not even telling a lie neither it was weird and scary, but I started instead of getting scared thinking about it I took interest in watching the movies more over and over. Strange I sure was when was a little girl growing up LOL!!!! xD