We have just rented an apartment which has an internal ’Chatzer’, i.e. it’s a room in the middle of the house without a roof. Instead of a roof there are a few (5-6) narrow slats crossing from one side to the other. Could we simply lay Schach on top and convert this room into a Sukka?

Theoretically you can use your Chatzer for a Sukkah. However there are a few Halachic requirements you must fit, for the Sukkah to be kosher. It depends what is the distance between the opening in roof and the walls, if it's more than 1.92M it's no good, it depends also the material of the slats, the distance between them and their width. Since there is more to it I will recommend to have a rabbi or a learned person check it out for you. Chag Sameach