I usually see fireplaces that are open only on one side. This would be a standard example:
The flames are surrounded by 3 walls and open on the one viewing side. Recently I've noticed some fireplaces such as:
These are open on three sides. Does this mean it would be possible to have a fireplace in the middle of a room that is completely open on all sides, with only a chimney? I suspect you would want some sort of protective screen for debris and such.