Looks like a cast iron/steel part, most likely made in china. Not sure where or if you could find a exact replacement.
If your handy with a drill, I could tell you how to repair this.

To me it looks a little heavy duty to be made in China. Do you know the name of the manufacturer. You could call them for the part. Just a shot but this type of wooden framed Canadian Glider is made by Dutalier of Canada their number is 450-772-2432. Post a better picture of the whole chair. Maybe someone can identify it if you don't know the name of the manufacturer.

Even though it looks like a thick heavy part, a metallurgist might tell you different. Its easy to tell because of the texture of the part and the seams along the center. So this is not a forged steel part. Compare wrenches/tools from Snap-on and Harbor Freight to get a good example of what im talking about.