The Ashtray Maze is an elaborate maze located in the upper Research Sector in the Oldest House. Created by the Ashtray Object of Power, the maze is designed to prevent unauthorized persons from accessing the Dimensional Research laboratory and the Hedron chamber. However, the maze can be navigated with the aid of Ahti's cassette player. The maze itself is generated by the Ashtray and Cigarette Object of Power, and permits only the one whom is bound to the OoP (As well as those they designate) to pass through the maze. Other individuals attempting to traverse the maze presumably become lost within, or — in the case of Jesse prior to obtaining Ahti's cassette player — are only able to exit where they entered. It is known that there are civilians lost in the maze from prior to the Ashtray's retrieval by the FBC.
The Ashtray OoP itself is bound to Director Trench, though it is not made clear what effects his death has on this binding. It is possible that Jesse's initial attempt to traverse the maze returned her to the entrance because of Trench's death or because she had taken over as director. Hiss are encountered in the maze, but they seem to be focused on attacking Jesse rather than traversing the maze itself. Additionally, the maze in several instances prevents the Hiss from being able to reach Jesse — this indicates that the maze perhaps protects those with traversal privileges.
It is not fully clear whether Ahti was given permission by Trench to traverse, whether his cassette player conveys this, or whether some supernatural ability inherent to Ahti allows it (Though it is likely one of the latter considering researchers were surprised at Ahti's ability to make it through the maze as noted in the Janitor Complaint).
The first traversal by Jesse allows the player to fully experience the maze. Subsequent traversals teleport the player to near the end and back to the entrance.