Mothman

As the story goes-

At least one of the Mothman sightings involved car chases. The creature was reported to have at first been on the side of the road. It then spread wings and (without flapping them once) rise straight up in the air like a helicopter would. No matter how fast the driver dared to speed in an attempt to get away Mothman always kept pace.

Just imagine something huge, seemingly headless, with wings that never move, and two large red eyes buzzing your car at seventy mph or higher!