The Twilight Zone, Season 5

Rod Serling:
This is the face of terror: Anne Marie Henderson, eighteen years of age, her young existence suddenly marred by a savage and wholly unanticipated pursuit by a strange, nightmarish figure of a woman in black, who has appeared as if from nowhere and now at driving gallop chases the terrified girl across the countryside, as if she means to ride her down and kill her - and then suddenly and inexplicably stops, to watch in malignant silence as her prey takes flight. Miss Henderson has no idea whatever as to the motive for this pursuit; worse, not the vaguest notion regarding the identity of her pursuer. Soon enough, she will be given the solution to this twofold mystery, but in a manner far beyond her present capacity to understand, a manner enigmatically bizarre in terms of time and space - which is to say, an answer from the Twilight Zone.