Take a picture of the light and take it to a local lighting store (not Lowes or HD) and ask them if it can be done. They should give you advice and assistance with products if it is possible.

It depends on the exact construction of the light but it is probably possible. I have seen some lights which came in a kit designed for mounting either as a chandelier or direct to the box.

Most lights are built with standard sized threaded rods and fittings. You might be able to unscrew the ceiling plate from the light fixture, then screw on a loop piece. Then the chandelier chain runs from that loop to another loop that goes through the hole in the original ceiling plate and screws into the threaded bracket in the ceiling which is attached to the electrical box. You may need an additional flat or bowl shaped cover, depending on the fixture. Of course, you will need to rewire the fixture by replacing the wires from the box into the light with a cord long enough to reach through the chain.

Your cheapest source of parts is probably an old hanging fixture from a thrift store, goodwill or a garage sale. Buying your parts from the lighting or hardware store will probably turn out to be almost as much money as buying a new light fixture. Plus, the exercise in taking apart the old fixture will help you see how to adapt your fixture. Unless you really love your current fixture, this might be a good time to buy a different light.

If you can post a good closeup picture, I can give you more ideas

Thank you for your suggestions. I've attached 2 photos of the light. The nook is within the dining room where I've hung a full size chandelier over the table, and there is some chain left over. I bought this light to go in the nook because the dimensions were just right for the 6' x 6' area and it was the smallest ceiling light fixture (15" diameter) in the collection (Gala by Hampton Bay). Also, there was already a place to hang a fixture in the ceiling, there was just a plate covering it. But the semi-flushmount makes it so close to the ceiling that the arch in the opening hides it, and it floods the whole area with light, rather than making it feel more cozy/intimate.

I'll try to find a place that can do the conversion. I hope I don't have to buy another fixture. I like this one.

From what I can see, that shouldn't be a problem. However, if you aren't doing it yourself with salvage parts, it might be cheaper to buy a new fixture.

That room looks similar style, color and window size to my dining room The major difference is my side window is 6 over 6 and yours is 6 over 1. I understand why you would want to keep the fixture as it can be a real hunt to find a fixture which looks right for the space in an older house.