A tray table assembly adapted to move to and from a stowed position in a stowage module positioned to one side of a passenger seat. The assembly includes an arcuate rail movably mounted in the stowage module, a tray table mounted on the rail for arcuate movement along the rail between the stowed position and the deployed position relative to the rail, and also mounted on the rail for fore and aft translating movement in the deployed position. The tray table rides on an arcuate rail that permits both deployment and fore and aft movement of the tray table, and automatically centers the tray table during movement toward the stowed position.