Do you mean a rod that spans the entire space or one that is connected to only one wall? If the latter, you might be fighting the law of physics. A light with any weight on the end of a long rod like that would probably pull the rod downward and either pull it out of the wall or bend it, unless you have some pretty substantial bracing in the wall.

As far as the chandelier wire cutting across the view from the balcony, we have this in our dining room, which has an upstairs gallery/balcony on one side and very tall windows on the other. You really don't notice the chain -- in fact, in a way, it ties the space together. I think a horizontal rod would be more intrusive.

It's the half rod. I agree it will need to be very strong, but we have access to a good solid wall so we can bolt it down. The first challenge is finding a rod rather than having to make one myself.

Thanks for the opinion on the chain.

You might also consider some of the newer low voltage lights that hang from a pair of wires from wall to wall.
The wires are both mechanical support for the small lights and power conductors.

You can place the lights anywhere along the wires, and even place more than one light close to another to light a larger area.

The wires are small enough to not be very noticeable.