Here's what I used:
I used two sizes of wire, 20 and 24 gauge (I couldn't find my 24 ga gunmetal, so I used bright silver. If it bothers me, I'll paint it!), fine gunmetal finish chain and square section toothpicks. I painted the toothpicks brown, then drilled holes in the first step and every other step after that. I put the toothpicks in place, then made a little loop of the silver wire, put it through the chain at an appropriate point and glued it (with Quick Grip :) to the toothpick. Then I made a larger loop of the thicker wire to add detail and to help keep the smaller chain-holding wire loop in place. I did that 10 times :)
The above photo shows the view from the front before I glued the charcoal burner unit in place. This is the last time I'll be able to see the stairs like this!
The above photo is one of the possible views of the staircase now that everything has been glued into place. It's from the left side door. Ignore the chain dangling down in the photo -- that's the leftover chain at the top of the staircase which I'm keeping until I see how much chain I need for the final handrail support on the first floor.
And the final photo is what is visible of the staircase from the front of the kitchen wing. I'm really glad I added the handrail!