Of course, the ghost itself is a character. It could be a former inhabitant of the place, like a long - dead nobleman or a servant who met a tragic end. And there could be other secondary characters like the protagonist's friends who either believe or don't believe in the existence of the ghost and their reactions add to the story's drama.
Perhaps it's a story about a vengeful ghost. The ghost might have been wronged in the past and now it's seeking revenge on those who did it harm. It could be wandering around, scaring people who cross its path. For example, it might appear in front of someone in a dark alley and give them a terrifying look.
I'm not entirely sure which specific ghost story Chie tells in that instance. There are so many interesting stories in Persona 4 Golden that it's hard to recall this one off the top of my head.
Maybe it's the sudden appearance of the ghost in the story. Just imagine, in the dark night, a shadowy figure suddenly emerges from nowhere, that would be really terrifying.
Well, often there could be a spooky old house. Maybe a strange noise that comes at midnight, like creaking floors. And there might be a shadowy figure that lurks in the dark corners.